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On Algebraic and Geometric Dimensions for Groups with Torsion
Author(s) -
Brady Noel,
Leary Ian J.,
Nucinkis Brita E. A.
Publication year - 2001
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s002461070100240x
Subject(s) - contractible space , mathematics , counterexample , conjecture , pure mathematics , discrete group , finite group , group (periodic table) , generalization , algebraic number , torsion (gastropod) , algebraic group , fixed point , combinatorics , algebra over a field , mathematical analysis , physics , medicine , surgery , quantum mechanics
Various notions of dimension for discrete groups are compared. A group is exhibited that acts with finite stabilizers on an acyclic 2‐complex in such a way that the fixed point subcomplex for any non‐trivial finite subgroup is contractible, but such that the group does not admit any such action on a contractible 2‐complex. This group affords a counterexample to a natural generalization of the Eilenberg–Ganea conjecture.