Collinet, G., Djament, A. and Griffin, J. T. (2013) Stabilité homologique pour les groupes d'automorphismes des produits libres. International Mathematics Research Notices, 2013(19), pp. 4451-4476. (doi: 10.1093/imrn/rns181)
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Abstract
We show in this article that, for any group $G$ indecomposable for the free product * and non-isomorphic to $\mathbf{Z}$, the canonical inclusion ${\rm Aut}(G^{*n})\to {\rm Aut}(G^{* n+1})$ induces an isomorphism between the homology groups $H_i$ for $n\geq 2i+2$, as was conjectured by Hatcher and Wahl. In fact we show a little more --- in particular, the result is true for any group $G$ if we replace the automorphism group of the free product by the subgroup of symmetric automorphisms. For this purpose we use constructions and acyclicity results due to McCullough-Miller and Chen-Glover-Jensen and functoriality properties which allow us to apply classical methods in functor homology.
| Item Type: | Articles |
|---|---|
| Keywords: | Automorphism groups, homological stability, functor homology |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Griffin, Dr James |
| Authors: | Collinet, G., Djament, A., and Griffin, J. T. |
| Subjects: | Q Science > QA Mathematics |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | International Mathematics Research Notices |
| Publisher: | Oxford University Press |
| ISSN: | 1073-7928 |
| ISSN (Online): | 1687-0247 |
| Related URLs: |
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