Geometric And Cohomological Group Theory

Author: Peter H. Kropholler
Publisher: Cambridge University Press
ISBN: 131662322X
Size: 36.28 MB
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Surveys the state of the art in geometric and cohomological group theory. Ideal entry point for young researchers.

Geometric Group Theory

Author: Graham A. Niblo
Publisher: Cambridge University Press
ISBN: 9780521446808
Size: 55.55 MB
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The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. This second volume contains solely a ground breaking paper by Gromov, which provides a fascinating look at finitely generated groups. For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.

Two Dimensional Homotopy And Combinatorial Group Theory

Author: Cynthia Hog-Angeloni
Publisher: Cambridge University Press
ISBN: 9780521447003
Size: 38.86 MB
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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.

Geometric Group Theory

Author: Graham A. Niblo
Publisher: Cambridge University Press
ISBN: 9780521435291
Size: 36.31 MB
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For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library.

Geometry And Cohomology In Group Theory

Author: Peter H. Kropholler
Publisher: Cambridge University Press
ISBN: 9780521635561
Size: 47.21 MB
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This volume covers cohomology, representation theory, geometric and combinatorial group theory.

Topological Methods In Group Theory

Author: Ross Geoghegan
Publisher: Springer Science & Business Media
ISBN: 0387746110
Size: 21.98 MB
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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.

Homological Group Theory

Author: C. T. C. Wall
Publisher: Cambridge University Press
ISBN: 0521227291
Size: 22.21 MB
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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.

Algebraic Topology Via Differential Geometry

Author: M. Karoubi
Publisher: Cambridge University Press
ISBN: 9780521317146
Size: 48.77 MB
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In this volume the authors seek to illustrate how methods of differential geometry find application in the study of the topology of differential manifolds. Prerequisites are few since the authors take pains to set out the theory of differential forms and the algebra required. The reader is introduced to De Rham cohomology, and explicit and detailed calculations are present as examples. Topics covered include Mayer-Vietoris exact sequences, relative cohomology, Pioncare duality and Lefschetz's theorem. This book will be suitable for graduate students taking courses in algebraic topology and in differential topology. Mathematicians studying relativity and mathematical physics will find this an invaluable introduction to the techniques of differential geometry.

Combinatorial And Geometric Group Theory Edinburgh 1993

Author: Andrew J. Duncan
Publisher: Cambridge University Press
ISBN: 9780521465953
Size: 34.49 MB
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The ICMS Workshop on Geometric and Combinatorial Methods in Group Theory, held at Heriot-Watt University in 1993, brought together some of the leading research workers in the subject. Some of the survey articles and contributed papers presented at the meeting are collected in this volume. The former cover a number of areas of current interest and include papers by: S. M. Gersten, R. I. Grigorchuk, P. H. Kropholler, A. Lubotzky, A. A. Razborov and E. Zelmanov. The contributed articles, all refereed, range over a wide number of topics in combinatorial and geometric group theory and related topics. The volume represents a summary of the state of knowledge of the field, and as such will be indispensable to all research workers in the area.