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Algebra VII

Combinatorial Group Theory Applications to Geometry

  • Book
  • © 1993

Overview

Editors:
  1. A. N. Parshin

    1. Steklov Mathematical Institute, Moscow, Russia

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    You can also search for this editor in PubMed   Google Scholar

  2. I. R. Shafarevich

    1. Steklov Mathematical Institute, Moscow, Russia

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    You can also search for this editor in PubMed   Google Scholar

  • A comprehensive description of the roots of topology - Of great use to researchers in group theory and the topology of surfaces - Contains list of open problems, some of which have not been considered previously

Part of the book series: Encyclopaedia of Mathematical Sciences (EMS, volume 58)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-vii
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  2. Combinatorial Group Theory and Fundamental Groups

    1. Front Matter

      Pages 1-2
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    2. Introduction

      • A. N. Parshin
      Pages 3-5

    3. Group Presentations and 2-Complexes

      • A. N. Parshin
      Pages 6-31

    4. Free Groups and Free Products

      • A. N. Parshin
      Pages 31-61

    5. Surfaces and Planar Discontinuous Groups

      • A. N. Parshin
      Pages 61-90

    6. Cancellation Diagrams and Equations Over Groups

      • A. N. Parshin
      Pages 90-105

    7. 3-Manifolds and Knots

      • A. N. Parshin
      Pages 105-127

    8. Cohomological Methods and Ends

      • A. N. Parshin
      Pages 127-142

    9. Decision Problems

      • A. N. Parshin
      Pages 143-166

  3. Some Questions of Group Theory Related to Geometry

    1. Front Matter

      Pages 167-168
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    2. Introduction

      • A. N. Parshin
      Pages 169-171

    3. Equations in Groups and Some Related Questions

      • A. N. Parshin
      Pages 172-186

    4. Splitting Homomorphisms and Some Problems in Topology

      • A. N. Parshin
      Pages 187-208

    5. On the Rate of Growth of Groups and Amenable Groups

      • A. N. Parshin
      Pages 208-232

  4. Back Matter

    Pages 233-242
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Keywords

About this book

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

Reviews

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

Editors and Affiliations

  • Steklov Mathematical Institute, Moscow, Russia

    A. N. Parshin, I. R. Shafarevich

Bibliographic Information

  • Book Title: Algebra VII

  • Book Subtitle: Combinatorial Group Theory Applications to Geometry

  • Editors: A. N. Parshin, I. R. Shafarevich

  • Series Title: Encyclopaedia of Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-642-58013-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-54700-6Published: 23 September 1993

  • Softcover ISBN: 978-3-540-63704-2Published: 17 March 1998

  • eBook ISBN: 978-3-642-58013-0Published: 01 December 2013

  • Series ISSN: 0938-0396

  • Edition Number: 1

  • Number of Pages: VII, 242

  • Additional Information: Originally published as volume 58 in the series: Encyclopaedia of Mathematical Sciences

  • Topics: Group Theory and Generalizations, Algebraic Topology

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