Papers On Group Theory And Topology

Author : Max Dehn
Publisher : Springer Science & Business Media
Page : 404 pages
File Size : 50,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461246688

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Papers on Group Theory and Topology by Max Dehn Pdf

The work of Max Dehn (1878-1952) has been quietly influential in mathematics since the beginning of the 20th century. In 1900 he became the first to solve one of the famous Hilbert problems (the third, on the decomposition of polyhedra), in 1907 he collaborated with Heegaard to produce the first survey of topology, and in 1910 he began publishing his own investigations in topology and combinatorial group theory. His influence is apparent in the terms Dehn's algorithm, Dehn's lemma and Dehn surgery (and Dehnsche Gruppenbilder, generally known in English as Cayley diagrams), but direct access to his work has been difficult. No edition of his works has been produced, and some of his most important results were never published, at least not by him. The present volume is a modest attempt to bring Dehn's work to a wider audience, particularly topologists and group theorists curious about the origins of their subject and interested in mining the sources for new ideas. It consists of English translations of eight works : five of Dehn's major papers in topology and combinatorial group theory, and three unpublished works which illuminate the published papers and contain some results not available elsewhere. In addition, I have written a short introduction to each work, summarising its contents and trying to establish its place among related works of Dehn and others, and I have added an appendix on the Dehn-Nielsen theorem (often known simply as Nielsen's theorem) .

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243724

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Classical Topology and Combinatorial Group Theory by John Stillwell Pdf

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 nr~ understand the simplest topological facts, such as the rcason 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 development 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 recreations like the seven bridges; rather, it resulted from the l'isualization of problems from other parts of mathematics-complex analysis (Riemann), mechanics (Poincare), and group theory (Dehn). It is these connec tions to other parts of mathematics which make topology an important as well as a beautiful subject.

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 44,7 Mb
Release : 2007-12-17
Category : Mathematics
ISBN : 9780387746111

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Topological Methods in Group Theory by Ross Geoghegan Pdf

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Author : S. M. Gersten,John R. Stallings
Publisher : Princeton University Press
Page : 568 pages
File Size : 51,5 Mb
Release : 1987-05-21
Category : Mathematics
ISBN : 0691084106

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Combinatorial Group Theory and Topology by S. M. Gersten,John R. Stallings Pdf

Group theory and topology are closely related. The region of their interaction, combining the logical clarity of algebra with the depths of geometric intuition, is the subject of Combinatorial Group Theory and Topology. The work includes papers from a conference held in July 1984 at Alta Lodge, Utah. Contributors to the book include Roger Alperin, Hyman Bass, Max Benson, Joan S. Birman, Andrew J. Casson, Marshall Cohen, Donald J. Collins, Robert Craggs, Michael Dyer, Beno Eckmann, Stephen M. Gersten, Jane Gilman, Robert H. Gilman, Narain D. Gupta, John Hempel, James Howie, Roger Lyndon, Martin Lustig, Lee P. Neuwirth, Andrew J. Nicas, N. Patterson, John G. Ratcliffe, Frank Rimlinger, Caroline Series, John R. Stallings, C. W. Stark, and A. Royce Wolf.

Author : Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary
Publisher : Springer
Page : 174 pages
File Size : 49,7 Mb
Release : 2018-06-14
Category : Mathematics
ISBN : 3319828835

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Topology and Geometric Group Theory by Michael W. Davis,James Fowler,Jean-François Lafont,Ian J. Leary Pdf

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted. Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

Author : Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Publisher : CRC Press
Page : 188 pages
File Size : 46,7 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 9780203885765

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Applications of Group Theory to Combinatorics by Jack Koolen,Jin Ho Kwak,Ming-Yao Xu Pdf

Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state

Author : Taqdir Husain
Publisher : Courier Dover Publications
Page : 241 pages
File Size : 40,9 Mb
Release : 2018-02-15
Category : Mathematics
ISBN : 9780486819198

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Introduction to Topological Groups by Taqdir Husain Pdf

Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.

Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 51,7 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780387746142

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Topological Methods in Group Theory by Ross Geoghegan Pdf

This book is about the interplay between algebraic topology and the theory of infinite discrete groups. It is a hugely important contribution to the field of topological and geometric group theory, and is bound to become a standard reference in the field. To keep the length reasonable and the focus clear, the author assumes the reader knows or can easily learn the necessary algebra, but wants to see the topology done in detail. The central subject of the book is the theory of ends. Here the author adopts a new algebraic approach which is geometric in spirit.

Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 225 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209294

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Geometry of Surfaces by John Stillwell Pdf

The geometry of surfaces is an ideal starting point for learning geometry, for, among other reasons, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. This text provides the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. It includes exercises and informal discussions.

Author : Adam Clay,Dale Rolfsen
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 44,6 Mb
Release : 2016-11-16
Category : Knot theory
ISBN : 9781470431068

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Ordered Groups and Topology by Adam Clay,Dale Rolfsen Pdf

This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.

Author : Robert J. Zimmer
Publisher : University of Chicago Press
Page : 724 pages
File Size : 49,6 Mb
Release : 2019-12-23
Category : Mathematics
ISBN : 9780226568270

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Group Actions in Ergodic Theory, Geometry, and Topology by Robert J. Zimmer Pdf

Robert J. Zimmer is best known in mathematics for the highly influential conjectures and program that bear his name. Group Actions in Ergodic Theory, Geometry, and Topology: Selected Papers brings together some of the most significant writings by Zimmer, which lay out his program and contextualize his work over the course of his career. Zimmer’s body of work is remarkable in that it involves methods from a variety of mathematical disciplines, such as Lie theory, differential geometry, ergodic theory and dynamical systems, arithmetic groups, and topology, and at the same time offers a unifying perspective. After arriving at the University of Chicago in 1977, Zimmer extended his earlier research on ergodic group actions to prove his cocycle superrigidity theorem which proved to be a pivotal point in articulating and developing his program. Zimmer’s ideas opened the door to many others, and they continue to be actively employed in many domains related to group actions in ergodic theory, geometry, and topology. In addition to the selected papers themselves, this volume opens with a foreword by David Fisher, Alexander Lubotzky, and Gregory Margulis, as well as a substantial introductory essay by Zimmer recounting the course of his career in mathematics. The volume closes with an afterword by Fisher on the most recent developments around the Zimmer program.

Author : Charles Terence Clegg Wall
Publisher : Cambridge University Press
Page : 409 pages
File Size : 55,9 Mb
Release : 1979-12-27
Category : Mathematics
ISBN : 9780521227292

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Homological Group Theory by Charles Terence Clegg Wall Pdf

Eminent mathematicians have presented papers on homological and combinatorial techniques in group theory. The lectures are aimed at presenting in a unified way new developments in the area.

Author : Michael Davis
Publisher : Princeton University Press
Page : 601 pages
File Size : 55,9 Mb
Release : 2008
Category : Mathematics
ISBN : 9780691131382

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The Geometry and Topology of Coxeter Groups by Michael Davis Pdf

The Geometry and Topology of Coxeter Groups is a comprehensive and authoritative treatment of Coxeter groups from the viewpoint of geometric group theory. Groups generated by reflections are ubiquitous in mathematics, and there are classical examples of reflection groups in spherical, Euclidean, and hyperbolic geometry. Any Coxeter group can be realized as a group generated by reflection on a certain contractible cell complex, and this complex is the principal subject of this book. The book explains a theorem of Moussong that demonstrates that a polyhedral metric on this cell complex is nonpositively curved, meaning that Coxeter groups are "CAT(0) groups." The book describes the reflection group trick, one of the most potent sources of examples of aspherical manifolds. And the book discusses many important topics in geometric group theory and topology, including Hopf's theory of ends; contractible manifolds and homology spheres; the Poincaré Conjecture; and Gromov's theory of CAT(0) spaces and groups. Finally, the book examines connections between Coxeter groups and some of topology's most famous open problems concerning aspherical manifolds, such as the Euler Characteristic Conjecture and the Borel and Singer conjectures.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 52,6 Mb
Release : 1968-12-31
Category : Electronic
ISBN : 0821896423

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Thirteen Papers on Group Theory, Algebraic Geometry and Algebraic Topology by Anonim Pdf

Author : Alexander Arhangel’skii,Mikhail Tkachenko
Publisher : Springer Science & Business Media
Page : 794 pages
File Size : 55,5 Mb
Release : 2008-05-01
Category : Mathematics
ISBN : 9789491216350

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Topological Groups and Related Structures, An Introduction to Topological Algebra. by Alexander Arhangel’skii,Mikhail Tkachenko Pdf

Algebraandtopology,thetwofundamentaldomainsofmathematics,playcomplem- tary roles. Topology studies continuity and convergence and provides a general framework to study the concept of a limit. Much of topology is devoted to handling in?nite sets and in?nity itself; the methods developed are qualitative and, in a certain sense, irrational. - gebra studies all kinds of operations and provides a basis for algorithms and calculations. Very often, the methods here are ?nitistic in nature. Because of this difference in nature, algebra and topology have a strong tendency to develop independently, not in direct contact with each other. However, in applications, in higher level domains of mathematics, such as functional analysis, dynamical systems, representation theory, and others, topology and algebra come in contact most naturally. Many of the most important objects of mathematics represent a blend of algebraic and of topologicalstructures. Topologicalfunctionspacesandlineartopologicalspacesingeneral, topological groups and topological ?elds, transformation groups, topological lattices are objects of this kind. Very often an algebraic structure and a topology come naturally together; this is the case when they are both determined by the nature of the elements of the set considered (a group of transformations is a typical example). The rules that describe the relationship between a topology and an algebraic operation are almost always transparentandnatural—theoperationhastobecontinuous,jointlyorseparately.