# A Combinatorial Introduction to Topology Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more.

Author: Michael Henle

Publisher: Courier Corporation

ISBN: 0486679667

Category: Mathematics

Page: 310

View: 422

Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.
Categories: Mathematics

# Introduction to Topology The aim of the book is to give a broad introduction of topology to undergraduate students.

Author: Min Yan

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110378160

Category: Mathematics

Page: 249

View: 100

The aim of the book is to give a broad introduction of topology to undergraduate students. It covers the most important and useful parts of the point-set as well as the combinatorial topology. The development of the material is from simple to complex, concrete to abstract, and appeals to the intuition of readers. Attention is also paid to how topology is actually used in the other fields of mathematics. Over 150 illustrations, 160 examples and 600 exercises will help readers to practice and fully understand the subject. Contents: Set and Map Metric Space Graph Topology Topological Concepts Complex Topological Properties Surface Topics in Point Set Topology Index
Categories: Mathematics

# Classical Topology and Combinatorial Group Theory At any rate, this is the aim of the present book. In support of this view, I have followed the historical develop ment where practicable, since it clearly shows the influence of geometric thought at all stages.

Author:

Publisher: Springer Science & Business Media

ISBN: 9781468401103

Category: Mathematics

Page: 301

View: 534

In recent years, many students have been introduced to topology in high school mathematics. Having met the Mobius band, the seven bridges of Konigsberg, Euler's polyhedron formula, and knots, the student is led to expect that these picturesque ideas will come to full flower in university topology courses. What a disappointment "undergraduate topology" proves to be! In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does not understand the simplest topological facts, such as the reason why knots exist. In my opinion, a well-balanced introduction to topology should stress its intuitive geometric aspect, while admitting the legitimate interest that analysts and algebraists have in the subject. At any rate, this is the aim of the present book. In support of this view, I have followed the historical develop ment where practicable, since it clearly shows the influence of geometric thought at all stages. This is not to claim that topology received its main impetus from geometric recrea. ions like the seven bridges; rather, it resulted from the visualization of problems from other parts of mathematics complex analysis (Riemann), mechanics (poincare), and group theory (Oehn). It is these connections to other parts of mathematics which make topology an important as well as a beautiful subject.
Categories: Mathematics

# Invitation to Combinatorial Topology Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.

Author: Maurice Fréchet

Publisher: Courier Corporation

ISBN: 0486427862

Category: Mathematics

Page: 124

View: 715

Elementary text, accessible to anyone with a background in high school geometry, covers problems inherent to coloring maps, homeomorphism, applications of Descartes' theorem, topological polygons, more. Includes 108 figures. 1967 edition.
Categories: Mathematics

# Introduction to Topology Annotation The Description for this book, Introduction to Topology, will be forthcoming.

Author: Solomon Lefschetz

Publisher:

ISBN: UOM:39015077954710

Category: Topology

Page: 218

View: 169

Annotation The Description for this book, Introduction to Topology, will be forthcoming.
Categories: Topology

# An Introduction to Algebraic Topology 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.

Author: Joseph Rotman

Publisher: Springer Science & Business Media

ISBN: 0387966781

Category: Mathematics

Page: 438

View: 718

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.
Categories: Mathematics

# Ordered Sets This new edition shifts the primary focus to finite ordered sets, with results on infinite ordered sets presented toward the end of each chapter whenever possible.

Author: Bernd Schröder

Publisher: Birkhäuser

ISBN: 9783319297880

Category: Mathematics

Page: 420

View: 130

An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.
Categories: Mathematics

# Introduction to Combinatorial Torsions This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds.

Author: Vladimir Turaev

Publisher: Birkhäuser

ISBN: 9783034883214

Category: Mathematics

Page: 124

View: 358

This book is an introduction to combinatorial torsions of cellular spaces and manifolds with special emphasis on torsions of 3-dimensional manifolds. The first two chapters cover algebraic foundations of the theory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C. Whitehead, J. Milnor and the author. We also discuss connections between the torsions and the Alexander polynomials of links and 3-manifolds. The third (and last) chapter of the book deals with so-called refined torsions and the related additional structures on manifolds, specifically homological orientations and Euler structures. As an application, we give a construction of the multivariable Conway polynomial of links in homology 3-spheres. At the end of the book, we briefly describe the recent results of G. Meng, C.H. Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds. The exposition is aimed at students, professional mathematicians and physicists interested in combinatorial aspects of topology and/or in low dimensional topology. The necessary background for the reader includes the elementary basics of topology and homological algebra.
Categories: Mathematics

# Combinatorial Methods in Topology and Algebra This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013.

Author: Bruno Benedetti

Publisher: Springer

ISBN: 9783319201559

Category: Mathematics

Page: 227

View: 970

Combinatorics plays a prominent role in contemporary mathematics, due to the vibrant development it has experienced in the last two decades and its many interactions with other subjects. This book arises from the INdAM conference "CoMeTA 2013 - Combinatorial Methods in Topology and Algebra,'' which was held in Cortona in September 2013. The event brought together emerging and leading researchers at the crossroads of Combinatorics, Topology and Algebra, with a particular focus on new trends in subjects such as: hyperplane arrangements; discrete geometry and combinatorial topology; polytope theory and triangulations of manifolds; combinatorial algebraic geometry and commutative algebra; algebraic combinatorics; and combinatorial representation theory. The book is divided into two parts. The first expands on the topics discussed at the conference by providing additional background and explanations, while the second presents original contributions on new trends in the topics addressed by the conference.
Categories: Mathematics

# Library Recommendations for Undergraduate Mathematics Introduction to Algebraic Topology . Columbus , OH : Charles E . Merrill , 1969 . *
BLACKETT , DONALD W . Elementary Topology : A Combinatorial and Algebraic
Approach , New York , NY : Academic Press , 1982 . GIBLIN , P . J . Graphs ...

Author: Mathematical Association of America. Committee on the Undergraduate Program in Mathematics

Publisher: Mathematical Assn of Amer

ISBN: UOM:39015057374137

Category: Academic libraries

Page: 194

View: 465

Categories: Academic libraries

# An Introduction to Topology and Homotopy A combinatorial characterization by K . Reidemeister ( 1935 ) and a triangulation
result by E . Moise ( 1951 ) give this topological classification for the lens spaces :
Lpq = Lr , s if and only if p = r and q = ts = 1 ( mod p ) . Example 3 The lens ...

Author: Allan J. Sieradski

Publisher: Wadsworth Publishing Company

ISBN: UOM:39015042124829

Category: Homotopy theory.

Page: 479

View: 476

This text is an introduction to topology and homotopy. Topics are integrated into a coherent whole and developed slowly so students will not be overwhelmed.
Categories: Homotopy theory.

# Torus Actions and Their Applications in Topology and Combinatorics The book presents the study of torus actions on topological spaces is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology.

Author: V. M. Buchstaber

Publisher: American Mathematical Soc.

ISBN: 9780821831861

Category: Mathematics

Page: 144

View: 931

This book presents the study of torus actions on topological spaces that is presented as a bridge connecting combinatorial and convex geometry with commutative and homological algebra, algebraic geometry, and topology. This established link helps in understanding the geometry and topology of a space with torus action by studying the combinatorics of the space of orbits. Conversely, subtle properties of a combinatorial object can be realized by interpreting it as the orbit structure for a proper manifold or as a complex acted on by a torus. The latter can be a symplectic manifold with Hamiltonian torus action, a toric variety or manifold, a subspace arrangement complement, etc., while the combinatorial objects include simplicial and cubical complexes, polytopes, and arrangements.This approach also provides a natural topological interpretation in terms of torus actions of many constructions from commutative and homological algebra used in combinatorics. The exposition centers around the theory of moment-angle complexes, providing an effective way to study invariants of triangulations by methods of equivariant topology. The book includes many new and well-known open problems and would be suitable as a textbook. It will be useful for specialists both in topology and in combinatorics and will help to establish even tighter connections between the subjects involved.
Categories: Mathematics

# Surface Topology Authors ' preface It is our intention in this book to provide a simple , intuitively
based , and readable introduction to geometric topology ( often referred to as
rubber sheet geometry ) which , nevertheless , achieves significant and
interesting ...

Author: P. A. Firby

Publisher: Ellis Horwood Limited

ISBN: UOM:39015024909767

Category: Mathematics

Page: 220

View: 289

This textbook examines the topology of compact surfaces through the development of simple ideas in plane geometry. A variety of topics are linked with surface topology, such as graph theory, group theory and non-Euclidean geometry, in order to provide an overview of the mathematics involved.
Categories: Mathematics

# Basic Topology In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating.

Author: M.A. Armstrong

Publisher: Springer Science & Business Media

ISBN: 9781475717938

Category: Mathematics

Page: 251

View: 774

In this broad introduction to topology, the author searches for topological invariants of spaces, together with techniques for their calculating. Students with knowledge of real analysis, elementary group theory, and linear algebra will quickly become familiar with a wide variety of techniques and applications involving point-set, geometric, and algebraic topology. Over 139 illustrations and more than 350 problems of various difficulties help students gain a thorough understanding of the subject.
Categories: Mathematics

# International mathematical news ... Data : Log - Linear Models and Latent - Structure Analysis . Addison - Wesley ,
1979 , 472 p . G . Grätzer : Universal Algebra . 2nd edition . Springer - Verlag ,
1979 , 500 p . , DM 59 . — . ° M . Henle : A Combinatorial Introduction to Topology
.

Author:

Publisher:

ISBN: UCSD:31822020224010

Category: Mathematics

Page:

View: 351

Categories: Mathematics

# Blowups Slicings and Permutation Groups in Combinatorial Topology In this work, elements and concepts of algebraic geometry, such as blowups, Morse theory as well as group theory are translated into the field of combinatorial topology in order to establish new tools to study combinatorial manifolds.

Author: Jonathan Spreer

Publisher: Logos Verlag Berlin GmbH

ISBN: 9783832529833

Category: Mathematics

Page: 251

View: 975

Combinatorial topology is a field of research that lies in the intersection of geometric topology, combinatorics, algebraic topology and polytope theory. The main objects of interest are piecewise linear topological manifolds where the manifold is given as a simplicial complex with some additional combinatorial structure. These objects are called combinatorial manifolds. In this work, elements and concepts of algebraic geometry, such as blowups, Morse theory as well as group theory are translated into the field of combinatorial topology in order to establish new tools to study combinatorial manifolds. These tools are applied to triangulated surfaces, 3- and 4-manifolds with and without the help of a computer. Among other things, a new combinatorial triangulation of the K3 surface, combinatorial properties of normal surfaces, and new combinatorial triangulations of pseudomanifolds with multiply transitive automorphism group are presented.
Categories: Mathematics

# Choice HENLE , Michael . A combinatorial introduction to topology . W. H. Freeman ,
1979. 310p ill ( A series of books in mathematical sciences ) bibl index 78-14874
. 18.50 ISBN 0-7167-0083-2 . C.I.P. Most introductory topology books concentrate
...

Author:

Publisher:

ISBN: UCSC:32106005850372

Category: Academic libraries

Page:

View: 587

Categories: Academic libraries

# Using the Borsuk Ulam Theorem While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results.

Author: Ji?í Matou?ek

Publisher: Springer Science & Business Media

ISBN: 9783540003625

Category: Computers

Page: 196

View: 858

To the uninitiated, algebraic topology might seem fiendishly complex, but its utility is beyond doubt. This brilliant exposition goes back to basics to explain how the subject has been used to further our understanding in some key areas. A number of important results in combinatorics, discrete geometry, and theoretical computer science have been proved using algebraic topology. While the results are quite famous, their proofs are not so widely understood. This book is the first textbook treatment of a significant part of these results. It focuses on so-called equivariant methods, based on the Borsuk-Ulam theorem and its generalizations. The topological tools are intentionally kept on a very elementary level. No prior knowledge of algebraic topology is assumed, only a background in undergraduate mathematics, and the required topological notions and results are gradually explained.
Categories: Computers