Dimension of the Torelli group for Out(F_n)
Geometric Topology
2009-11-11 v1 Group Theory
Abstract
Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T_3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T_n is finitely generated.
Keywords
Cite
@article{arxiv.math/0603177,
title = {Dimension of the Torelli group for Out(F_n)},
author = {Mladen Bestvina and Kai-Uwe Bux and Dan Margalit},
journal= {arXiv preprint arXiv:math/0603177},
year = {2009}
}
Comments
27 pages, 9 figures