# Search Results for "graphs-surfaces-and-homology-third-edition"

## Graphs, Surfaces and Homology

**Author**: Peter Giblin**Publisher:**Cambridge University Press**ISBN:**1139491172**Category:**Mathematics**Page:**N.A**View:**5390

Homology theory is a powerful algebraic tool that is at the centre of current research in topology and its applications. This accessible textbook will appeal to mathematics students interested in the application of algebra to geometrical problems, specifically the study of surfaces (sphere, torus, Mobius band, Klein bottle). In this introduction to simplicial homology - the most easily digested version of homology theory - the author studies interesting geometrical problems, such as the structure of two-dimensional surfaces and the embedding of graphs in surfaces, using the minimum of algebraic machinery and including a version of Lefschetz duality. Assuming very little mathematical knowledge, the book provides a complete account of the algebra needed (abelian groups and presentations), and the development of the material is always carefully explained with proofs given in full detail. Numerous examples and exercises are also included, making this an ideal text for undergraduate courses or for self-study.

## Graphs, Surfaces and Homology

*An Introduction to Algebraic Topology*

**Author**: P. Giblin**Publisher:**Springer Science & Business Media**ISBN:**9400959532**Category:**Juvenile Nonfiction**Page:**329**View:**2175

viii homology groups. A weaker result, sufficient nevertheless for our purposes, is proved in Chapter 5, where the reader will also find some discussion of the need for a more powerful in variance theorem and a summary of the proof of such a theorem. Secondly the emphasis in this book is on low-dimensional examples the graphs and surfaces of the title since it is there that geometrical intuition has its roots. The goal of the book is the investigation in Chapter 9 of the properties of graphs in surfaces; some of the problems studied there are mentioned briefly in the Introduction, which contains an in formal survey of the material of the book. Many of the results of Chapter 9 do indeed generalize to higher dimensions (and the general machinery of simplicial homology theory is avai1able from earlier chapters) but I have confined myself to one example, namely the theorem that non-orientable closed surfaces do not embed in three-dimensional space. One of the principal results of Chapter 9, a version of Lefschetz duality, certainly generalizes, but for an effective presentation such a gener- ization needs cohomology theory. Apart from a brief mention in connexion with Kirchhoff's laws for an electrical network I do not use any cohomology here. Thirdly there are a number of digressions, whose purpose is rather to illuminate the central argument from a slight dis tance, than to contribute materially to its exposition.

## Real and Complex Singularities

**Author**: Ana Claudia Nabarro,Juan J. Nuño-Ballesteros,Raúl Oset Sinha,Maria Aparecida Soares Ruas**Publisher:**American Mathematical Soc.**ISBN:**1470422050**Category:**Differential geometry -- Classical differential geometry -- Classical differential geometry**Page:**355**View:**7963

This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)

## Electromagnetic Theory and Computation

*A Topological Approach*

**Author**: Paul Wolfgang Gross,P. Robert Kotiuga**Publisher:**Cambridge University Press**ISBN:**9780521801607**Category:**Mathematics**Page:**278**View:**4322

Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents. Appendices bridge the gap between the material presented and standard expositions of differential forms, Hodge decompositions, and tools for realizing representatives of homology classes as embedded manifolds.

## A First Course in Topology

*Continuity and Dimension*

**Author**: John McCleary**Publisher:**American Mathematical Soc.**ISBN:**0821838849**Category:**Mathematics**Page:**211**View:**6133

How many dimensions does our universe require for a comprehensive physical description? In 1905, Poincare argued philosophically about the necessity of the three familiar dimensions, while recent research is based on 11 dimensions or even 23 dimensions. The notion of dimension itself presented a basic problem to the pioneers of topology. Cantor asked if dimension was a topological feature of Euclidean space. To answer this question, some important topological ideas were introduced by Brouwer, giving shape to a subject whose development dominated the twentieth century. The basic notions in topology are varied and a comprehensive grounding in point-set topology, the definition and use of the fundamental group, and the beginnings of homology theory requires considerable time.The goal of this book is a focused introduction through these classical topics, aiming throughout at the classical result of the Invariance of Dimension. This text is based on the author's course given at Vassar College and is intended for advanced undergraduate students. It is suitable for a semester-long course on topology for students who have studied real analysis and linear algebra. It is also a good choice for a capstone course, senior seminar, or independent study.

## 3D Topography

*A Simplicial Complex-based Solution in a Spatial DBMS*

**Author**: Friso Penninga**Publisher:**N.A**ISBN:**N.A**Category:**Geomorphology**Page:**192**View:**1352

## Physiological Basis of Aging and Geriatrics, Third Edition

**Author**: S. Timiras Paola**Publisher:**CRC Press**ISBN:**N.A**Category:**Medical**Page:**326**View:**8840

Aging is an inevitable aspect of living. This book covers the aging process from a physiological viewpoint, examining all systems of the body and describing changes that occur with normal aging and in disease. Its primary focus is on humans, but some animal and in vitro research is included to explain mechanisms and theories of aging. Integrated aspects of aging (e.g., demography of aging) are considered, and preventive and interventive measures (pharmacology, diet, exercise) for ensuring healthful aging are discussed. The Second Edition of Physiological Basis of Aging and Geriatrics considers many new approaches and methods for studying the aging process. New and updated information on molecular and cellular mechanisms, pathology, and aging-related diseases is provided to promote a better understanding of basic biological mechanisms. Theories, epidemiology, demographics, and comparative and differential aging are also presented.

## Computational Topology

*An Introduction*

**Author**: Herbert Edelsbrunner,John Harer**Publisher:**American Mathematical Soc.**ISBN:**0821849255**Category:**Mathematics**Page:**241**View:**8115

Combining concepts from topology and algorithms, this book delivers what its title promises: an introduction to the field of computational topology. Starting with motivating problems in both mathematics and computer science and building up from classic topics in geometric and algebraic topology, the third part of the text advances to persistent homology. This point of view is critically important in turning a mostly theoretical field of mathematics into one that is relevant to a multitude of disciplines in the sciences and engineering. The main approach is the discovery of topology through algorithms. The book is ideal for teaching a graduate or advanced undergraduate course in computational topology, as it develops all the background of both the mathematical and algorithmic aspects of the subject from first principles. Thus the text could serve equally well in a course taught in a mathematics department or computer science department.

## International Journal of Electrical Engineering Education

**Author**: N.A**Publisher:**N.A**ISBN:**N.A**Category:**Electric engineering**Page:**N.A**View:**4306