Summary
2011 International Symposium on Nonlinear Theory and Its Applications
2011
Session Number:A3L-C
Session:
Number:A3L-C3
Combinatorial Configuration Spaces
Dai Tamaki,
pp.200-203
Publication Date:2011/9/4
Online ISSN:2188-5079
Summary:
The notion of cellular stratified spaces was introduced in [BGRT] with the aim of constructing a cellular model of the configuration space of a sphere. In particular, it was shown that the classifying space (order complex) of the face poset of a totally normal regular cellular stratified space X can be embedded in X as a deformation retract. Here we elaborate on this idea and prove an extension of one of the main results in [BGRT]. We construct an acyclic category, called the face category, F(X) from a totally normal cellular stratified space X. We show the classifying space of F(X) can be embedded into X as a strong deformation retract. As an application, we construct a combinatorial model for the configuration space Confk(Γ) of k distinct points for any graph (1-dimensional finite cell complex) Γ.