Algebraic and Geometric Topology 4 (2004),
paper no. 15, pages 273-296.
A lower bound to the action dimension of a group
Sung Yil Yoon
Abstract.
The action dimension of a discrete group G, actdim(G), is defined to
be the smallest integer m such that G admits a properly discontinuous
action on a contractible m-manifold. If no such m exists, we define
actdim(G) = infty. Bestvina, Kapovich, and Kleiner used Van Kampen's
theory of embedding obstruction to provide a lower bound to the action
dimension of a group. In this article, another lower bound to the
action dimension of a group is obtained by extending their work, and
the action dimensions of the fundamental groups of certain manifolds
are found by computing this new lower bound.
Keywords.
Fundamental group, contractible manifold, action dimension, embedding obstruction
AMS subject classification.
Primary: 20F65.
Secondary: 57M60.
DOI: 10.2140/agt.2004.4.273
E-print: arXiv:math.GR/0405421
Submitted: 28 March 2003.
Accepted: 9 February 2004.
Published: 25 April 2004.
Notes on file formats
Sung Yil Yoon
110 8th Street RPI, Troy, NY 12180, USA
Email: yoons@rpi.edu
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