Papers On Group Theory And Topology

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Topological Methods In Group Theory

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Author : Ross Geoghegan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-17

Topological Methods In Group Theory written by Ross Geoghegan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-17 with Mathematics categories.

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.

Papers On Group Theory And Topology

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Author : Max Dehn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Papers On Group Theory And Topology written by Max Dehn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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) .

Classical Topology And Combinatorial Group Theory

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Author : John Stillwell
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Classical Topology And Combinatorial Group Theory written by John Stillwell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Combinatorial Group Theory And Topology

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Author : S. M. Gersten
language : en
Publisher: Princeton University Press
Release Date : 1987-05-21

Combinatorial Group Theory And Topology written by S. M. Gersten and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-05-21 with Mathematics categories.

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.

Combinatorial Group Theory

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Author : Daniel E. Cohen
language : en
Publisher: Cambridge University Press
Release Date : 1989-08-17

Combinatorial Group Theory written by Daniel E. Cohen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-08-17 with Mathematics categories.

In this book the author aims to show the value of using topological methods in combinatorial group theory.

Thirteen Papers On Group Theory Algebraic Geometry And Algebraic Topology

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Author :
language : en
Publisher: American Mathematical Soc.
Release Date : 1968-12-31

Thirteen Papers On Group Theory Algebraic Geometry And Algebraic Topology written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-12-31 with categories.

Ordered Groups And Topology

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Author : Adam Clay
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-11-16

Ordered Groups And Topology written by Adam Clay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-11-16 with Mathematics categories.

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.

Topological Groups And Related Structures An Introduction To Topological Algebra

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Author : Alexander Arhangel’skii
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-01

Topological Groups And Related Structures An Introduction To Topological Algebra written by Alexander Arhangel’skii and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-01 with Mathematics categories.

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.

Geometric Group Theory

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Author : Clara Löh
language : en
Publisher: Springer
Release Date : 2017-12-19

Geometric Group Theory written by Clara Löh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-19 with Mathematics categories.

Inspired by classical geometry, geometric group theory has in turn provided a variety of applications to geometry, topology, group theory, number theory and graph theory. This carefully written textbook provides a rigorous introduction to this rapidly evolving field whose methods have proven to be powerful tools in neighbouring fields such as geometric topology. Geometric group theory is the study of finitely generated groups via the geometry of their associated Cayley graphs. It turns out that the essence of the geometry of such groups is captured in the key notion of quasi-isometry, a large-scale version of isometry whose invariants include growth types, curvature conditions, boundary constructions, and amenability. This book covers the foundations of quasi-geometry of groups at an advanced undergraduate level. The subject is illustrated by many elementary examples, outlooks on applications, as well as an extensive collection of exercises.

Applications Of Group Theory To Combinatorics

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Author : Jack Koolen
language : en
Publisher: CRC Press
Release Date : 2008-07-02

Applications Of Group Theory To Combinatorics written by Jack Koolen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-02 with Mathematics categories.

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