Geometry and Cohomology in Group Theory

doi:10.1017/CBO9780511666131

This volume reflects the fruitful connections between group theory and topology. It contains articles on cohomology, representation theory, geometric and combinatorial group theory. Some of the world's best known figures in this very active area of mathematics have made contributions, including substantial articles from Ol'shanskii, Mikhajlovskii, Carlson, Benson, Linnell, Wilson and Grigorchuk, which will be valuable reference works for some years to come. Pure mathematicians working in the fields of algebra, topology, and their interactions, will find this book of great interest.

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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
- By Peter H. Kropholler, School of Mathematical Sciences Queen Mary & Westfield College Mile End Road London El 4NS, Graham A. Niblo, Faculty of Mathematical Studies University of Southampton Highfield Southampton SO17 1BJ, Ralph Stöhr, Mathematics Department UMIST P.O. Box 88 Manchester M60 1QD
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List of Participants
pp ix-xii
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On the Cohomology of SL2(ℤ[1/p])
pp 1-9
- By A. Adem, Mathematics Department, University of Wisconsin, Madison, WI 53706 USA., N. Naffah, Department of Mathematics, ETH–Zürich, Zürich CH–8092.
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Cohomology of Sporadic Groups, Finite Loop Spaces, and the Dickson Invariants
pp 10-23
- By D. J. Benson, Department of Mathematics, University of Georgia, Athens GA 30602, USA djb@byrd.math.uga.edu
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Kernels of Actions on Non-positively Curved Spaces
pp 24-38
- By R. Bieri, Fachbereich Mathematik,Department of Mathematical Sciences, Universitat Frankfurt, Robert-Mayer-Str. 6, D 6000, Frankfurt 1, Germany. email:bieri@math.uni-frankfurt.de, R. Geoghegan, State University of New York, Binghamton, NY 13902-6000, USA. email:ross@math.binghamton.edu
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Cyclic Groups Acting on Free Lie Algebras
pp 39-44
- By R. M. Bryant, Department of Mathematics, UMIST, P. O. Box 88, Manchester, M60 1QD.
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Cohomology, Representations and Quotient Categories of Modules
pp 45-73
- By J. F. Carlson, Department of Mathematics, University of Georgia, Athens, Georgia 30602. email:jfc@sloth.math.uga.edu
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Protrees and Λ-trees
pp 74-87
- By I.M. Chiswell, School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London El 4NS.
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Homological Techniques for Strongly Graded Rings: A Survey
pp 88-107
- By J. Cornick, Department of Mathematics, The Ohio State University, 231 W18th Avenue, Columbus, Ohio 43210, USA. email:cornick@math.ohio-state.edu
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Buildings are CAT(0)
pp 108-123
- By M. W. Davis, Department of Mathematics, The Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210 email:mdavis@math.ohio-state.edu
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On Subgroups of Coxeter Groups
pp 124-160
- By W. Dicks, Departament de Matematiques, Universitat Autonoma de Barcelona, E 08193, Bellaterra (Barcelona), Spain., I. J. Leary, Faculty of Mathematical Studies, University of Southampton, Southampton SO17 1BJ, England.
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The p-primary Farrell Cohomology of Out(Fp–1)
pp 161-169
- By H.H. Glover, Ohio State University, Columbus, Ohio email:glover@math.ohio-state.edu, G. Mislin, ETH Zürich, Switzerland and Ohio State University, Columbus, Ohio email:mislin@math.ethz.ch and mislin@math.ohio-state.edu, S.N. Voon, Ohio State University, Newark, Ohio email:snvoon@math.ohio-state.edu
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On Tychonoff Groups
pp 170-187
- By R.I. Grigorchuk
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Word Growth of Coxeter Groups
pp 188-189
- By D. L. Johnson, Mathematics Department, University of Nottingham, University Park, Nottingham.
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Poly-surface Groups
pp 190-208
- By F.E.A. Johnson, Department of Mathematics, University College London, Gower Street, London, WC1E 6BT.
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Analytic Versions of the Zero Divisor Conjecture
pp 209-248
- By P. A. Linnell, Math, VPI, Blacksburg, VA 24061–0123, USA email: linnell@math.vt.edu
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On the Geometric Invariants of Soluble Groups of Finite Prüfer Rank
pp 249-262
- By H. Meinert, Fachbereich Mathematik der Johann Wolfgang Goethe-Universität, Robert-Mayer-Str. 6–10, D-60054 Frankfurt a.M., Germany
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Some Constructions Relating to Hyperbolic Groups
pp 263-290
- By K.V. Mikhajlovskii, A. YU. Ol'shanskii
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Free Actions of Abelian Groups on Groups
pp 291-295
- By P. M. Neumann, Queen's College, Oxford, 0X1 4AW., P. J. Rowley, UMIST, Manchester, M60 1QD.
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Finitely Presented Soluble Groups
pp 296-316
- By J. S. Wilson
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Geometry and Cohomology in Group Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

List of Participants
pp ix-xii

On the Cohomology of SL2(ℤ[1/p])
pp 1-9

Cohomology of Sporadic Groups, Finite Loop Spaces, and the Dickson Invariants
pp 10-23

Kernels of Actions on Non-positively Curved Spaces
pp 24-38

Cyclic Groups Acting on Free Lie Algebras
pp 39-44

Cohomology, Representations and Quotient Categories of Modules
pp 45-73

Protrees and Λ-trees
pp 74-87

Homological Techniques for Strongly Graded Rings: A Survey
pp 88-107

Buildings are CAT(0)
pp 108-123

On Subgroups of Coxeter Groups
pp 124-160

The p-primary Farrell Cohomology of Out(Fp–1)
pp 161-169

On Tychonoff Groups
pp 170-187

Word Growth of Coxeter Groups
pp 188-189

Poly-surface Groups
pp 190-208

Analytic Versions of the Zero Divisor Conjecture
pp 209-248

On the Geometric Invariants of Soluble Groups of Finite Prüfer Rank
pp 249-262

Some Constructions Relating to Hyperbolic Groups
pp 263-290

Free Actions of Abelian Groups on Groups
pp 291-295

Finitely Presented Soluble Groups
pp 296-316

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Geometry and Cohomology in Group Theory

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