Homological stability for families of Coxeter groups Article Swipe
YOU?
·
· 2016
· Open Access
·
· DOI: https://doi.org/10.2140/agt.2016.16.2779
· OA: W1765655366
We prove that certain families of Coxeter groups and inclusions\n$W_1\\hookrightarrow W_2\\hookrightarrow...$ satisfy homological stability,\nmeaning that in each degree the homology $H_\\ast(BW_n)$ is eventually\nindependent of $n$. This gives a uniform treatment of homological stability for\nthe families of Coxeter groups of type $A_n$, $B_n$ and $D_n$, recovering\nexisting results in the first two cases, and giving a new result in the third.\nThe key step in our proof is to show that a certain simplicial complex with\n$W_n$-action is highly connected. To do this we show that the barycentric\nsubdivision is an instance of the 'basic construction', and then use Davis's\ndescription of the basic construction as an increasing union of chambers to\ndeduce the required connectivity.\n
