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.

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Sung Yil Yoon
110 8th Street RPI, Troy, NY 12180, USA

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