Homology representations arising from the half cube

Details Homology representations arising from the half cube Homology representations arising from the half cube

2008-06-09

arxiv.org/abs/0806.1503v2

Mathematics

Geometric Topology

Approximately 35 pages, AMSTeX. Revised in light of referee's comments. To appear in Advances in Mathematics

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Homology representations arising from the half cube does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Homology representations arising from the half cube, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homology representations arising from the half cube will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-401508