On Algebraic and Geometric Dimensions for Groups with Torsion | Zendy

Brady Noel | Zendy; Leary Ian J. | Zendy; Nucinkis Brita E. A. | Zendy

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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.

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