Homotopy Type of the Boolean Complex of a Coxeter System

Details Homotopy Type of the Boolean Complex of a Coxeter System Homotopy Type of the Boolean Complex of a Coxeter System

2008-06-05

arxiv.org/abs/0806.0906v3

Mathematics

Combinatorics

final version, to appear in Advances in Mathematics

Scientific paper

In any Coxeter group, the set of elements whose principal order ideals are boolean forms a simplicial poset under the Bruhat order. This simplicial poset defines a cell complex, called the boolean complex. In this paper it is shown that, for any Coxeter system of rank n, the boolean complex is homotopy equivalent to a wedge of (n-1)-dimensional spheres. The number of such spheres can be computed recursively from the unlabeled Coxeter graph, and defines a new graph invariant called the boolean number. Specific calculations of the boolean number are given for all finite and affine irreducible Coxeter systems, as well as for systems with graphs that are disconnected, complete, or stars. One implication of these results is that the boolean complex is contractible if and only if a generator of the Coxeter system is in the center of the group. of these results is that the boolean complex is contractible if and only if a generator of the Coxeter system is in the center of the group.

Affiliated with

Also associated with

No associations

Rating

Homotopy Type of the Boolean Complex of a Coxeter System 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 Homotopy Type of the Boolean Complex of a Coxeter System, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Homotopy Type of the Boolean Complex of a Coxeter System will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-127690