Volume 4, issue 1 (2004)

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A lower bound to the action dimension of a group

Sung Yil Yoon

Algebraic & Geometric Topology 4 (2004) 273–296

arXiv: math.GR/0405421


The action dimension of a discrete group Γ, actdim(Γ), is defined to be the smallest integer m such that Γ admits a properly discontinuous action on a contractible m–manifold. If no such m exists, we define actdim(Γ) . 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.

fundamental group, contractible manifold, action dimension, embedding obstruction
Mathematical Subject Classification 2000
Primary: 20F65
Secondary: 57M60
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Received: 28 March 2003
Accepted: 9 February 2004
Published: 25 April 2004
Sung Yil Yoon
110 8th Street RPI
Troy NY 12180