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© 1993

Algebra VII

Combinatorial Group Theory Applications to Geometry

  • A. N. Parshin
  • I. R. Shafarevich
Book
  • 7.5k Downloads

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

Table of contents

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

    1. Front Matter
      Pages 1-2
    2. A. N. Parshin
      Pages 3-5
    3. A. N. Parshin
      Pages 6-31
    4. A. N. Parshin
      Pages 31-61
    5. A. N. Parshin
      Pages 61-90
    6. A. N. Parshin
      Pages 105-127
    7. A. N. Parshin
      Pages 127-142
    8. A. N. Parshin
      Pages 143-166
  3. Some Questions of Group Theory Related to Geometry

    1. Front Matter
      Pages 167-168
    2. A. N. Parshin
      Pages 169-171
  4. Back Matter
    Pages 233-242

About this book

Introduction

From the reviews of the first printing of this book, published as volume 58 of the Encyclopaedia of Mathematical Sciences:
"... This book will be very useful as a reference and guide to researchers and graduate students in algebra and and topology." Acta Scientiarum Mathematicarum, Ungarn, 1994 "... The book under review consists of two monographs on geometric aspects of group theory: Combinatorial group theory and fundamental groups" by D.J.Collins and H.Zieschang ...: "Some problems of group theory related to geometry" by R.I.Grigorchuk and P.F.Kurchanov. ... 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. ... In summary, a very interesting book! Bulletin of the London Mathematical Society, 1996 "... In both essays the authors give clear and comprehensive definitions, examples and statements (but not proofs) of theorems, so that the book can be understood by a reader with a minimal background in group theory or geometry. Such a reader, needing to find out what is known in this area, will find this a full and accessible store of information." Contemporary Physics, 1994 "...This survey (Part II) presents for the first time that problems in monograph form and by the way offers a unifying treatment of the various approaches to their solutions, as far as they are known, together with hints to open problems. A titbit for every interested reader!" Monatshefte für Mathematik, 1995

Keywords

algebraic topology group theory algebra automorphism cohomology Fundamental group Group theory homology Homotopy

Editors and affiliations

  • A. N. Parshin
    • 1
  • I. R. Shafarevich
    • 1
  1. 1.Steklov Mathematical InstituteMoscowRussia

Bibliographic information

  • Book Title Algebra VII
  • Book Subtitle Combinatorial Group Theory Applications to Geometry
  • Authors D.J. Collins
    R.I. Grigorchuk
    P.F. Kurchanov
    H. Zieschang
  • Editors A.I. Kostrikin
    I.R. Shafarevich
  • Series Title Encyclopaedia of Mathematical Sciences
  • DOI https://doi.org/10.1007/978-3-642-58013-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-54700-6
  • Softcover ISBN 978-3-540-63704-2
  • eBook ISBN 978-3-642-58013-0
  • Series ISSN 0938-0396
  • Edition Number 1
  • Number of Pages VII, 242
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Additional Information Originally published as volume 58 in the series: Encyclopaedia of Mathematical Sciences
  • Topics Group Theory and Generalizations
    Algebraic Topology
  • Buy this book on publisher's site

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