Homology representations arising from the half cube
| dc.creator | Green, R. M. | |
| dc.date | 2008-06-09 | |
| dc.date | 2008-12-04 | |
| dc.date.accessioned | 2026-07-07T12:08:58Z | |
| dc.date.available | 2026-07-07T12:08:58Z | |
| dc.description | We construct a CW decomposition $C_n$ of the $n$-dimensional half cube in a manner compatible with its structure as a polytope. For each $3 \leq k \leq n$, the complex $C_n$ has a subcomplex $C_{n, k}$, which coincides with the clique complex of the half cube graph if $k = 4$. The homology of $C_{n, k}$ is concentrated in degree $k-1$ and furthermore, the $(k-1)$-st Betti number of $C_{n, k}$ is equal to the $(k-2)$-nd Betti number of the complement of the $k$-equal real hyperplane arrangement. These Betti numbers, which also appear in theoretical computer science, numerical analysis and engineering, are the coefficients of a certain Pascal-like triangle (Sloane's sequence A119258). The Coxeter groups of type $D_n$ act naturally on the complexes $C_{n, k}$, and thus on the associated homology groups. | |
| dc.description | Approximately 35 pages, AMSTeX. Revised in light of referee's comments. To appear in Advances in Mathematics | |
| dc.identifier | https://arxiv.org/abs/0806.1503 | |
| dc.identifier | http://arxiv.org/abs/0806.1503 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209475 | |
| dc.subject | Geometric Topology | |
| dc.subject | Combinatorics | |
| dc.subject | 05E25, 52B11, 57Q05 | |
| dc.title | Homology representations arising from the half cube | |
| dc.type | text |