Search results for: algebraic-and-geometric-topology

Algebraic and Geometric Topology

Author : R. James Milgram
File Size : 33.46 MB
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Contains sections on Structure of topological manifolds, Low dimensional manifolds, Geometry of differential manifolds and algebraic varieties, $H$-spaces, loop spaces and $CW$ complexes, Problems.

Algebraic and Geometric Topology

Author : Andrew Ranicki
File Size : 36.91 MB
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Algebraic and Geometric Topology

Author : R. James Milgram
File Size : 75.30 MB
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Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.

Algebraic and Geometric Topology

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File Size : 25.62 MB
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Techniques of Geometric Topology

Author : Roger Fenn
File Size : 23.69 MB
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Lecture Notes in Algebraic Topology

Author : James Frederic Davis
File Size : 28.11 MB
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The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the ``big picture'', teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Algebraic and Geometric Topology

Author : R. James Milgram
File Size : 42.37 MB
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Contains sections on Algebraic $K$- and $L$-theory, Surgery and its applications, Group actions.

Issues in Algebra Geometry and Topology 2011 Edition

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File Size : 71.94 MB
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Issues in Algebra, Geometry, and Topology / 2011 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Algebra, Geometry, and Topology. The editors have built Issues in Algebra, Geometry, and Topology: 2011 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Algebra, Geometry, and Topology in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in Algebra, Geometry, and Topology: 2011 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.

Algebraic and Geometric Topology

Author : Kenneth C. Millett
File Size : 62.59 MB
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Perspectives in Analysis Geometry and Topology

Author : Ilia Itenberg
File Size : 30.56 MB
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The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.