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Author : John Stillwell
Publisher : Unknown
Page : 301 pages
File Size : 46,8 Mb
Release : 1980
Category : Combinatorial group theory
ISBN : 750620102X
Author : John Stillwell
Publisher : Springer Science & Business Media
Page : 344 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461243724
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 : S. M. Gersten,John R. Stallings
Publisher : Princeton University Press
Page : 564 pages
File Size : 43,9 Mb
Release : 1987-05-21
Category : Mathematics
ISBN : 9780691084107
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 : Paul Latiolais
Publisher : Unknown
Page : 220 pages
File Size : 46,9 Mb
Release : 2014-09-01
Category : Electronic
ISBN : 3662210940
Author : Paul Latiolais
Publisher : Springer
Page : 215 pages
File Size : 45,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540462965
This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. Many of the ideas presented are still in their infancy, and it is hoped that the work here will spur others to new and exciting developments. Among the many techniques disussed are the use of obstruction groups to distinguish certain exact sequences and several graph theoretic techniques with applications to the theory of groups.
Author : Gilbert Baumslag
Publisher : Birkhäuser
Page : 174 pages
File Size : 40,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034885874
Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. With surprising frequency, problems in a wide variety of disciplines, including differential equations, automorphic functions and geometry, have been distilled into explicit questions about groups, typically of the following kind: Are the groups in a given class finite (e.g., the Burnside problem)? Finitely generated? Finitely presented? What are the conjugates of a given element in a given group? What are the subgroups of that group? Is there an algorithm for deciding for every pair of groups in a given class whether they are isomorphic or not? The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. In view of the scope of the subject and the extraordinary variety of groups involved, it is not surprising that no really general theory exists. These notes, bridging the very beginning of the theory to new results and developments, are devoted to a number of topics in combinatorial group theory and serve as an introduction to the subject on the graduate level.
Author : S. M. Gersten
Publisher : Unknown
Page : 551 pages
File Size : 42,5 Mb
Release : 1987
Category : Electronic
ISBN : OCLC:859811233
Author : Daniel E. Cohen
Publisher : Cambridge University Press
Page : 325 pages
File Size : 40,8 Mb
Release : 1989-08-17
Category : Mathematics
ISBN : 9780521341332
In this book the author aims to show the value of using topological methods in combinatorial group theory.
Author : Roger C. Lyndon,Paul E. Schupp
Publisher : Springer
Page : 354 pages
File Size : 42,8 Mb
Release : 2015-03-12
Category : Mathematics
ISBN : 9783642618963
From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Author : Ross Geoghegan
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 53,8 Mb
Release : 2007-12-27
Category : Mathematics
ISBN : 9780387746142
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 : Jack Koolen,Jin Ho Kwak,Ming-Yao Xu
Publisher : CRC Press
Page : 188 pages
File Size : 54,5 Mb
Release : 2008-07-02
Category : Mathematics
ISBN : 9780203885765
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 : Vladimir Shpilrain,Alexander Mikhalev,Jie-tai Yu
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 40,5 Mb
Release : 2012-11-12
Category : Mathematics
ISBN : 9780387217246
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.
Author : D.J. Collins,R.I. Grigorchuk,P.F. Kurchanov,H. Zieschang
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 48,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642580130
From the reviews: "... The book under review consists of two monographs on geometric aspects of group theory ... Together, these two articles form a wide-ranging survey of combinatorial group theory, with emphasis very much on the geometric roots of the subject. This will be a useful reference work for the expert, as well as providing an overview of the subject for the outsider or novice. Many different topics are described and explored, with the main results presented but not proved. This allows the interested reader to get the flavour of these topics without becoming bogged down in detail. Both articles give comprehensive bibliographies, so that it is possible to use this book as the starting point for a more detailed study of a particular topic of interest. ..." Bulletin of the London Mathematical Society, 1996
Author : Cynthia Hog-Angeloni,Wolfgang Metzler,Allan J. Sieradski
Publisher : Cambridge University Press
Page : 428 pages
File Size : 54,7 Mb
Release : 1993-12-09
Category : Mathematics
ISBN : 9780521447003
Basic work on two-dimensional homotopy theory dates back to K. Reidemeister and J. H. C. Whitehead. Much work in this area has been done since then, and this book considers the current state of knowledge in all the aspects of the subject. The editors start with introductory chapters on low-dimensional topology, covering both the geometric and algebraic sides of the subject, the latter including crossed modules, Reidemeister-Peiffer identities, and a concrete and modern discussion of Whitehead's algebraic classification of 2-dimensional homotopy types. Further chapters have been skilfully selected and woven together to form a coherent picture. The latest algebraic results and their applications to 3- and 4-dimensional manifolds are dealt with. The geometric nature of the subject is illustrated to the full by over 100 diagrams. Final chapters summarize and contribute to the present status of the conjectures of Zeeman, Whitehead, and Andrews-Curtis. No other book covers all these topics. Some of the material here has been used in courses, making this book valuable for anyone with an interest in two-dimensional homotopy theory, from graduate students to research workers.
Author : Benjamin Fine,Anthony M. Gaglione
Publisher : American Mathematical Soc.
Page : 191 pages
File Size : 53,9 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851166
The AMS Special Session on Combinatorial Group Theory--Infinite Groups, held at the University of Maryland in April 1988, was designed to draw together researchers in various areas of infinite group theory, especially combinatorial group theory, to share methods and results. The session reflected the vitality and interests in infinite group theory, with eighteen speakers presenting lectures covering a wide range of group-theoretic topics, from purely logical questions to geometric methods. The heightened interest in classical combinatorial group theory was reflected in the sheer volume of work presented during the session. This book consists of eighteen papers presented during the session. Comprising a mix of pure research and exposition, the papers should be sufficiently understandable to the nonspecialist to convey a sense of the direction of this field. However, the volume will be of special interest to researchers in infinite group theory and combinatorial group theory, as well as to those interested in low-dimensional (especially three-manifold) topology.