A lower bound to the action dimension of a group

Details A lower bound to the action dimension of a group A lower bound to the action dimension of a group

2004-05-21

arxiv.org/abs/math/0405421v1

Algebr. Geom. Topol. 4 (2004) 273-296

Mathematics

Group Theory

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-15.abs.html

Scientific paper

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.

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