Geodesic
A lower bound to the action dimension of a group
Yoon, Sung Yil1
1110 8th Street RPI, Troy NY 12180, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 273-296
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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.

DOI : 10.2140/agt.2004.4.273
Keywords: fundamental group, contractible manifold, action dimension, embedding obstruction

Yoon, Sung Yil  1

1 110 8th Street RPI, Troy NY 12180, USA 
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Yoon, Sung Yil. A lower bound to the action dimension of a group. Algebraic and Geometric Topology, Tome 4 (2004) no. 1, pp. 273-296. doi: 10.2140/agt.2004.4.273

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