Project C8: Finiteness Properties of Infinite Discrete Groups
| Principal Investigator(s) |
Summary:
The main goal is to establish finiteness properties (finite generation, finte presentability, etc.)
of arithmetic groups in positive characteristic, e.g., $SL_N(\mathbf{F}_q[t; t^{-1}])$. In particular, one aim is a
proof of the {\em Rank Conjecture} which would give the exact finiteness length for reductive groups.
Another point on the agenda is the question whether $SL_2(\mathbf{Z}[t; t^{-1}])$ is finitely generated. Finally
the finiteness properties of Torelli subgroups (a) in Out($F_{N}$) and (b) in mappingclass groups of
closed oriented surfaces are to be determined.
Recent Preprints:
13030
Barbara Baumeister, Matthias Grüninger PDF
Polytopes and groups
Project:
C8
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12146
Kai-Uwe Bux, Martin Georg Fluch, Marco Marschler, Stefan Witzel PDF
The braided Thompson’s groups are of type $F_\infty$
Project:
C8
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The braided Thompson’s groups are of type $F_\infty$
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12145
PDF
Higher generation for pure braid groups
Project:
C8
X
Higher generation for pure braid groups
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12070
Martin Georg Fluch, Marco Marschler, Stefan Witzel, Matthew Zaremsky PDF
The Brin-Thompson groups $sV$ are of type $F_\infty$
Project:
C8
To appear: Pacific J. Math. (2013)
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The Brin-Thompson groups $sV$ are of type $F_\infty$
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12069
Martin Georg Fluch, Ian Leary PDF
An Eilenberg–Ganea phenomenon for actions with virtually cyclic stabilisers
Project:
C8
To appear: Groups Geom. Dyn. (2013)
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An Eilenberg–Ganea phenomenon for actions with virtually cyclic stabilisers
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12060
Kai-Uwe Bux, Ralf Köhl, Stefan Witzel PDF
Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: The Rank Theorem
Project:
C8
Published: Annals of Math. 177 (2013), 311-366
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Higher Finiteness Properties of Reductive Arithmetic Groups in Positive Characteristic: The Rank Theorem
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12055
PDF
Rational homological stability for groups of partially symmetric automorphisms of free groups
Project:
C8
X
Rational homological stability for groups of partially symmetric automorphisms of free groups
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12054
Robert McEwen PDF
A combinatorial proof of the degree theorem in Auter space
Project:
C8
X
A combinatorial proof of the degree theorem in Auter space
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12053
Martin Georg Fluch, Stefan Witzel PDF
Brown's criterion in Bredon homology
Project:
C8
To appear: Homology Homotopy Appl. (2013)
X
Brown's criterion in Bredon homology
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12004
Martin Georg Fluch, Brita Nucinkis PDF
On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups
Project:
C8
To appear: Proc. Amer. Math. Soc. (2013)
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On the classifying space for the family of virtually cyclic subgroups for elementary amenable groups
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