Search Results for "topology-and-geometry-graduate-texts-in-mathematics"

Maß und Kategorie

Maß und Kategorie

  • Author: J.C. Oxtoby
  • Publisher: Springer-Verlag
  • ISBN: 364296074X
  • Category: Mathematics
  • Page: 112
  • View: 6173
DOWNLOAD NOW »
Dieses Buch behandelt hauptsächlich zwei Themenkreise: Der Bairesche Kategorie-Satz als Hilfsmittel für Existenzbeweise sowie Die "Dualität" zwischen Maß und Kategorie. Die Kategorie-Methode wird durch viele typische Anwendungen erläutert; die Analogie, die zwischen Maß und Kategorie besteht, wird nach den verschiedensten Richtungen hin genauer untersucht. Hierzu findet der Leser eine kurze Einführung in die Grundlagen der metrischen Topologie; außerdem werden grundlegende Eigenschaften des Lebesgue schen Maßes hergeleitet. Es zeigt sich, daß die Lebesguesche Integrationstheorie für unsere Zwecke nicht erforderlich ist, sondern daß das Riemannsche Integral ausreicht. Weiter werden einige Begriffe aus der allgemeinen Maßtheorie und Topologie eingeführt; dies geschieht jedoch nicht nur der größeren Allgemeinheit wegen. Es erübrigt sich fast zu erwähnen, daß sich die Bezeichnung "Kategorie" stets auf "Bairesche Kategorie" be zieht; sie hat nichts zu tun mit dem in der homologischen Algebra verwendeten Begriff der Kategorie. Beim Leser werden lediglich grundlegende Kenntnisse aus der Analysis und eine gewisse Vertrautheit mit der Mengenlehre vorausgesetzt. Für die hier untersuchten Probleme bietet sich in natürlicher Weise die mengentheoretische Formulierung an. Das vorlie gende Buch ist als Einführung in dieses Gebiet der Analysis gedacht. Man könnte es als Ergänzung zur üblichen Grundvorlesung über reelle Analysis, als Grundlage für ein Se minar oder auch zum selbständigen Studium verwenden. Bei diesem Buch handelt es sich vorwiegend um eine zusammenfassende Darstellung; jedoch finden sich in ihm auch einige Verfeinerungen bekannter Resultate, namentlich Satz 15.6 und Aussage 20.4. Das Literaturverzeichnis erhebt keinen Anspruch auf Vollständigkeit. Häufig werden Werke zitiert, die weitere Literaturangaben enthalten.

Topology and Geometry

Topology and Geometry

  • Author: Glen E. Bredon
  • Publisher: Springer Science & Business Media
  • ISBN: 1475768486
  • Category: Mathematics
  • Page: 131
  • View: 3124
DOWNLOAD NOW »
This book offers an introductory course in algebraic topology. Starting with general topology, it discusses differentiable manifolds, cohomology, products and duality, the fundamental group, homology theory, and homotopy theory. From the reviews: "An interesting and original graduate text in topology and geometry...a good lecturer can use this text to create a fine course....A beginning graduate student can use this text to learn a great deal of mathematics."—-MATHEMATICAL REVIEWS

Differentialgeometrie, Topologie und Physik

Differentialgeometrie, Topologie und Physik

  • Author: Mikio Nakahara
  • Publisher: Springer-Verlag
  • ISBN: 3662453002
  • Category: Science
  • Page: 597
  • View: 2858
DOWNLOAD NOW »
Differentialgeometrie und Topologie sind wichtige Werkzeuge für die Theoretische Physik. Insbesondere finden sie Anwendung in den Gebieten der Astrophysik, der Teilchen- und Festkörperphysik. Das vorliegende beliebte Buch, das nun erstmals ins Deutsche übersetzt wurde, ist eine ideale Einführung für Masterstudenten und Forscher im Bereich der theoretischen und mathematischen Physik. - Im ersten Kapitel bietet das Buch einen Überblick über die Pfadintegralmethode und Eichtheorien. - Kapitel 2 beschäftigt sich mit den mathematischen Grundlagen von Abbildungen, Vektorräumen und der Topologie. - Die folgenden Kapitel beschäftigen sich mit fortgeschritteneren Konzepten der Geometrie und Topologie und diskutieren auch deren Anwendungen im Bereich der Flüssigkristalle, bei suprafluidem Helium, in der ART und der bosonischen Stringtheorie. - Daran anschließend findet eine Zusammenführung von Geometrie und Topologie statt: es geht um Faserbündel, characteristische Klassen und Indextheoreme (u.a. in Anwendung auf die supersymmetrische Quantenmechanik). - Die letzten beiden Kapitel widmen sich der spannendsten Anwendung von Geometrie und Topologie in der modernen Physik, nämlich den Eichfeldtheorien und der Analyse der Polakov'schen bosonischen Stringtheorie aus einer gemetrischen Perspektive. Mikio Nakahara studierte an der Universität Kyoto und am King’s in London Physik sowie klassische und Quantengravitationstheorie. Heute ist er Physikprofessor an der Kinki-Universität in Osaka (Japan), wo er u. a. über topologische Quantencomputer forscht. Diese Buch entstand aus einer Vorlesung, die er während Forschungsaufenthalten an der University of Sussex und an der Helsinki University of Sussex gehalten hat.

Topology

Topology

A Geometric Approach

  • Author: Terry Lawson
  • Publisher: Oxford University Press on Demand
  • ISBN: 9780199202485
  • Category: Mathematics
  • Page: 388
  • View: 8643
DOWNLOAD NOW »
This new-in-paperback introduction to topology emphasizes a geometric approach with a focus on surfaces. A primary feature is a large collection of exercises and projects, which fosters a teaching style that encourages the student to be an active class participant. A wide range of material at different levels supports flexible use of the book for a variety of students. Part I is appropriate for a one-semester or two-quarter course, and Part II (which is problem based) allows the book to be used for a year-long course which supports a variety of syllabuses. The over 750 exercises range from simple checks of omitted details in arguments, to reinforce the material and increase student involvement, to the development of substantial theorems that have been broken into many steps. The style encourages an active student role. Solutions to selected exercises are included as an appendix, with solutions to all exercises available to the instructor on a companion website.

Einführung in die Symplektische Geometrie

Einführung in die Symplektische Geometrie

  • Author: Rolf Berndt
  • Publisher: Springer-Verlag
  • ISBN: 9783322802156
  • Category: Mathematics
  • Page: 185
  • View: 4987
DOWNLOAD NOW »

Introduction to Topological Manifolds

Introduction to Topological Manifolds

  • Author: John Lee
  • Publisher: Springer Science & Business Media
  • ISBN: 1441979409
  • Category: Mathematics
  • Page: 433
  • View: 1599
DOWNLOAD NOW »
This book is an introduction to manifolds at the beginning graduate level, and accessible to any student who has completed a solid undergraduate degree in mathematics. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Although this second edition has the same basic structure as the first edition, it has been extensively revised and clarified; not a single page has been left untouched. The major changes include a new introduction to CW complexes (replacing most of the material on simplicial complexes in Chapter 5); expanded treatments of manifolds with boundary, local compactness, group actions, and proper maps; and a new section on paracompactness.

Convex Integration Theory

Convex Integration Theory

Solutions to the h-principle in geometry and topology

  • Author: David Spring
  • Publisher: Springer Science & Business Media
  • ISBN: 3034800606
  • Category: Mathematics
  • Page: 213
  • View: 8227
DOWNLOAD NOW »
§1. Historical Remarks Convex Integration theory, ?rst introduced by M. Gromov [17], is one of three general methods in immersion-theoretic topology for solving a broad range of problems in geometry and topology. The other methods are: (i) Removal of Singularities, introduced by M. Gromov and Y. Eliashberg [8]; (ii) the covering homotopy method which, following M. Gromov’s thesis [16], is also referred to as the method of sheaves. The covering homotopy method is due originally to S. Smale [36] who proved a crucial covering homotopy result in order to solve the classi?cation problem for immersions of spheres in Euclidean space. These general methods are not linearly related in the sense that succ- sive methods subsumed the previous methods. Each method has its own distinct foundation, based on an independent geometrical or analytical insight. Con- quently, each method has a range of applications to problems in topology that are best suited to its particular insight. For example, a distinguishing feature of ConvexIntegrationtheoryisthatitappliestosolveclosed relationsinjetspaces, including certain general classes of underdetermined non-linear systems of par- 1 tial di?erential equations. As a case of interest, the Nash-Kuiper C -isometric immersion theorem can be reformulated and proved using Convex Integration theory (cf. Gromov [18]). No such results on closed relations in jet spaces can be proved by means of the other two methods. On the other hand, many classical results in immersion-theoretic topology, such as the classi?cation of immersions, are provable by all three methods.

Homotopical Topology

Homotopical Topology

  • Author: Anatoly Fomenko,Dmitry Fuchs
  • Publisher: Springer
  • ISBN: 3319234889
  • Category: Mathematics
  • Page: 627
  • View: 5683
DOWNLOAD NOW »
This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).

Geometric Topology in Dimensions 2 and 3

Geometric Topology in Dimensions 2 and 3

  • Author: E.E. Moise
  • Publisher: Springer Science & Business Media
  • ISBN: 1461299063
  • Category: Mathematics
  • Page: 262
  • View: 1688
DOWNLOAD NOW »
Geometric topology may roughly be described as the branch of the topology of manifolds which deals with questions of the existence of homeomorphisms. Only in fairly recent years has this sort of topology achieved a sufficiently high development to be given a name, but its beginnings are easy to identify. The first classic result was the SchOnflies theorem (1910), which asserts that every 1-sphere in the plane is the boundary of a 2-cell. In the next few decades, the most notable affirmative results were the "Schonflies theorem" for polyhedral 2-spheres in space, proved by J. W. Alexander [Ad, and the triangulation theorem for 2-manifolds, proved by T. Rad6 [Rd. But the most striking results of the 1920s were negative. In 1921 Louis Antoine [A ] published an extraordinary paper in which he 4 showed that a variety of plausible conjectures in the topology of 3-space were false. Thus, a (topological) Cantor set in 3-space need not have a simply connected complement; therefore a Cantor set can be imbedded in 3-space in at least two essentially different ways; a topological 2-sphere in 3-space need not be the boundary of a 3-cell; given two disjoint 2-spheres in 3-space, there is not necessarily any third 2-sphere which separates them from one another in 3-space; and so on and on. The well-known "horned sphere" of Alexander [A ] appeared soon thereafter.

Lecture Notes on Elementary Topology and Geometry

Lecture Notes on Elementary Topology and Geometry

  • Author: I.M. Singer,J.A. Thorpe
  • Publisher: Springer
  • ISBN: 1461573475
  • Category: Mathematics
  • Page: 232
  • View: 5747
DOWNLOAD NOW »
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

An Introduction to Algebraic Topology

An Introduction to Algebraic Topology

  • Author: Joseph J. Rotman
  • Publisher: Springer Science & Business Media
  • ISBN: 1461245761
  • Category: Mathematics
  • Page: 437
  • View: 2860
DOWNLOAD NOW »
A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

Eichfeldtheorie

Eichfeldtheorie

Eine Einführung in die Differentialgeometrie auf Faserbündeln

  • Author: Helga Baum
  • Publisher: Springer-Verlag
  • ISBN: 3642385397
  • Category: Mathematics
  • Page: 380
  • View: 4991
DOWNLOAD NOW »
Dieses Lehrbuch bietet eine Einführung in die Differentialgeometrie auf Faserbündeln. Nach einem Kapitel über Lie-Gruppen und homogene Räume werden lokal-triviale Faserungen, insbesondere die Hauptfaserbündel und zu ihnen assoziierte Vektorbündel, besprochen. Es folgen die grundlegenden Begriffe der Differentialrechnung auf Faserbündeln: Zusammenhang, Krümmung, Parallelverschiebung und kovariante Ableitung. Anschließend werden die Holonomiegruppen vorgestellt, die zentrale Bedeutung in der Differentialgeometrie haben. Als Anwendungen werden charakteristische Klassen und die Yang-Mills-Gleichung behandelt. Zahlreiche Aufgaben mit Lösungshinweisen helfen, das Gelernte zu vertiefen. Das Buch richtet sich vor allem an Studenten der Mathematik und Physik im Masterstudium. Es stellt mathematische Grundlagen bereit, die in Vorlesungen zur Eichfeldtheorie in der theoretischen und mathematischen Physik Anwendung finden.

Einführung in die Funktionalanalysis

Einführung in die Funktionalanalysis

  • Author: Reinhold Meise,Dietmar Vogt
  • Publisher: Springer-Verlag
  • ISBN: 3322803104
  • Category: Mathematics
  • Page: 416
  • View: 3769
DOWNLOAD NOW »
Dieses Buch wendet sich an Studenten der Mathematik und der Physik, welche über Grundkenntnisse in Analysis und linearer Algebra verfügen.

Lineare Darstellungen endlicher Gruppen

Lineare Darstellungen endlicher Gruppen

  • Author: Jean Pierre Serre
  • Publisher: Springer-Verlag
  • ISBN: 3322858634
  • Category: Mathematics
  • Page: 102
  • View: 4930
DOWNLOAD NOW »

A Basic Course in Algebraic Topology

A Basic Course in Algebraic Topology

  • Author: William S. Massey
  • Publisher: Springer Science & Business Media
  • ISBN: 9780387974309
  • Category: Mathematics
  • Page: 428
  • View: 4191
DOWNLOAD NOW »
This textbook is intended for a course in algebraic topology at the beginning graduate level. The main topics covered are the classification of compact 2-manifolds, the fundamental group, covering spaces, singular homology theory, and singular cohomology theory. These topics are developed systematically, avoiding all unnecessary definitions, terminology, and technical machinery. The text consists of material from the first five chapters of the author's earlier book, Algebraic Topology; an Introduction (GTM 56) together with almost all of his book, Singular Homology Theory (GTM 70). The material from the two earlier books has been substantially revised, corrected, and brought up to date.

Differential Topology

Differential Topology

  • Author: Morris W. Hirsch
  • Publisher: Springer Science & Business Media
  • ISBN: 146849449X
  • Category: Mathematics
  • Page: 222
  • View: 1663
DOWNLOAD NOW »
"A very valuable book. In little over 200 pages, it presents a well-organized and surprisingly comprehensive treatment of most of the basic material in differential topology, as far as is accessible without the methods of algebraic topology....There is an abundance of exercises, which supply many beautiful examples and much interesting additional information, and help the reader to become thoroughly familiar with the material of the main text." —MATHEMATICAL REVIEWS

Introduction to Topological Manifolds

Introduction to Topological Manifolds

  • Author: John M. Lee
  • Publisher: Springer Science & Business Media
  • ISBN: 038722727X
  • Category: Mathematics
  • Page: 392
  • View: 6415
DOWNLOAD NOW »
Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Manuscripta mathematica

Manuscripta mathematica

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category:
  • Page: N.A
  • View: 1974
DOWNLOAD NOW »

Geometry & Topology

Geometry & Topology

  • Author: N.A
  • Publisher: N.A
  • ISBN: N.A
  • Category: Geometry
  • Page: N.A
  • View: 384
DOWNLOAD NOW »
Fully refereed international journal dealing with all aspects of geometry and topology and their applications.

Real and Abstract Analysis

Real and Abstract Analysis

A modern treatment of the theory of functions of a real variable

  • Author: Edwin Hewitt,Karl Stromberg
  • Publisher: Springer-Verlag
  • ISBN: 3662297949
  • Category: Mathematics
  • Page: 476
  • View: 7430
DOWNLOAD NOW »