Homology of holomorphs of free groups

Craig A. Jensen

Homology of holomorphs of free groups

Group Theory 2007-05-23 v2 Algebraic Topology

Authors: Craig A. Jensen

Abstract

The holomorph of a free group $F_n$ is the semidirect product $F_n \rtimes Aut(F_n)$ . Using the methods of Hatcher and Vogtmann, we derive stability results and calculate the mod- $p$ homology of these holomorphs for odd primes $p$ in dimensions 1 and 2, and their rational homology in dimensions 1 through 5. Calculations of the twisted (where $Aut(F_n)$ acts by first projecting to $Gl_n(\Z)$ and then including in $Gl_n(\Q)$ ) homology $H_*(Aut(F_n); \Q^n)$ follow in corresponding dimensions.

Keywords

holomorph of free group semidirect product mod-p homology rational homology twisted homology stability

Cite

@article{arxiv.math/0112187,
  title  = {Homology of holomorphs of free groups},
  author = {Craig A. Jensen},
  journal= {arXiv preprint arXiv:math/0112187},
  year   = {2007}
}

Comments

Revised using helpful comments of referee. Accepted by J. Algebra. J. Algebra has agreed to host the Maple program files (currently on my web page) on their site

Homology of holomorphs of free groups

Abstract

Keywords

Cite

Comments

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