Models for Configuration Space in a Simplicial Complex

Abstract

We produce combinatorial models for configuration space in a simplicial complex, and for configurations near a single point ("local configuration space.") The model for local configuration space is built out of the poset of poset structures on a finite set. The model for global configuration space relies on a combinatorial model for a simplicial complex with a deleted subcomplex. By way of application, we study the nodal curve $y^{2}z=x^3+x^{2}z$, obtaining a presentation for its two-strand braid group, a conjectural presentation for its three-strand braid group, and presentations for its two- and three-strand local braid groups near the singular point.

11 pages, 1 figure

Cited by in corpus (1)

• Asymptotic homology of graph braid groups