A lower bound to the action dimension of a group
Group Theory
2014-10-01 v1
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
Cite
@article{arxiv.math/0405421,
title = {A lower bound to the action dimension of a group},
author = {Sung Yil Yoon},
journal= {arXiv preprint arXiv:math/0405421},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-15.abs.html