Homological Group Theory

C. T. C. Wall

doi:10.1017/CBO9781107325449

In 1977 several eminent mathematicians were invited to Durham to present papers at a short conference on homological and combinatorial techniques in group theory. The lectures, published here, aimed at presenting in a unified way new developments in the area. Group theory is approached from a geometrical viewpoint and much of the material has not previously been published. The various ways in which topological ideas can be used in group theory are also brought together. The volume concludes with an extensive set of problems, ranging from explicit questions demanding detailed calculation to fundamental questions motivating research in the area. These lectures will be of interest mainly to researchers in pure mathematics but will also prove useful in connection with relevant postgraduate courses.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
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Introduction
pp ix-x
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1 - Traces and Euler characteristics
pp 1-26
- By Hyman Bass, Columbia University
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2 - Groups of virtually finite dimension
pp 27-70
- By Kenneth S. Brown, Cornell University
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3 - Free abelianised extensions of finite groups
pp 71-104
- By K. W. Gruenberg, Queen Mary College, London
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4 - Arithmetic groups
pp 105-136
- By J.-P. Serre, Collège de France, Alan Robinson, Colin MacLachlan
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5 - Topological methods in group theory
pp 137-204
- By Peter Scott, University of Liverpool, Terry Wall, University of Liverpool
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6 - An example of a finite presented solvable group
pp 205-212
- By Herbert Abels, Universität Bielefeld
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7 - SL3(Fq[t]) is not finitely presentable
pp 213-224
- By Helmut Behr, Universität Frankfurt am Main
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8 - Two-dimensional Poincaré duality groups and pairs
pp 225-230
- By Robert Bieri, Universität Freiburg im Brg. and Eth Zürich, Beno Eckmann, Universität Freiburg im Brg. and Eth Zürich
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9 - Metabelian quotients of finitely presented soluble groups are finitely presented
pp 231-234
- By Robert Bieri, Freiburg University, Ralph Strebel, Heidelberg University
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10 - Soluble groups with coherent group rings
pp 235-240
- By Robert Bieri, Freiburg University, Ralph Strebel, Heidelberg University
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11 - Cohomological aspects of 2-graphs. II
pp 241-244
- By Peter J. Cameron, Oxford University
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12 - Recognizing free factors
pp 245-250
- By M. J. Dunwoody, University of Sussex
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13 - Trees of homotopy types of ( m)-complexes
pp 251-254
- By Micheal Dyer, University of Oregon
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14 - Geometric structure of surface mapping class groups
pp 255-270
- By W. J. Harvey, Institute for Advanced Study
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15 - Cohomology theory of aspherical groups and of small cancellation groups
pp 271-274
- By Johannes Huebschmann, University of Heidelberg
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16 - Finite groups of deficiency zero
pp 275-290
- By D. L. Johnson, University of Nottingham, E. F. Robertson, University of St Andrews
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17 - Äquivalenzklassen von Gruppenbeschreibungen, Identitäten und einfacher Homotopietyp in niederen Dimensionen
pp 291-326
- By Wolfgang Metzler, University of Frankfurt
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18 - Two-dimensional complexes with torsion values not realizable by self-equivalences
pp 327-338
- By Wolfgang Metzler, University of Frankfurt
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19 - Applications of Nielsen's reduction method to the solution of combinatorial problems in group theory: a survey
pp 339-358
- By Gerhard Rosenberger, University of Dortmund
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20 - Chevalley groups over polynomial rings
pp 359-368
- By Christophe Soulé, University of Paris VII
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List of problems
pp 369-394
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Homological Group Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Introduction
pp ix-x

1 - Traces and Euler characteristics
pp 1-26

2 - Groups of virtually finite dimension
pp 27-70

3 - Free abelianised extensions of finite groups
pp 71-104

4 - Arithmetic groups
pp 105-136

5 - Topological methods in group theory
pp 137-204

6 - An example of a finite presented solvable group
pp 205-212

7 - SL3(Fq[t]) is not finitely presentable
pp 213-224

8 - Two-dimensional Poincaré duality groups and pairs
pp 225-230

9 - Metabelian quotients of finitely presented soluble groups are finitely presented
pp 231-234

10 - Soluble groups with coherent group rings
pp 235-240

11 - Cohomological aspects of 2-graphs. II
pp 241-244

12 - Recognizing free factors
pp 245-250

13 - Trees of homotopy types of ( m)-complexes
pp 251-254

14 - Geometric structure of surface mapping class groups
pp 255-270

15 - Cohomology theory of aspherical groups and of small cancellation groups
pp 271-274

16 - Finite groups of deficiency zero
pp 275-290

17 - Äquivalenzklassen von Gruppenbeschreibungen, Identitäten und einfacher Homotopietyp in niederen Dimensionen
pp 291-326

18 - Two-dimensional complexes with torsion values not realizable by self-equivalences
pp 327-338

19 - Applications of Nielsen's reduction method to the solution of combinatorial problems in group theory: a survey
pp 339-358

20 - Chevalley groups over polynomial rings
pp 359-368

List of problems
pp 369-394

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Homological Group Theory

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