  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.
