Abrams's stable equivalence for graph braid groups

Abstract

In his PhD thesis, Abrams proved that, for a natural number n and a graph G with at least n vertices, the n-strand configuration space of G deformation retracts to a compact subspace, the discretized n-strand configuration space, provided G satisfies two conditions: each path between distinct essential vertices (vertices of degree not equal to 2) is of length at least n+1 edges, and each path from a vertex to itself which is not nullhomotopic is of length at least n+1 edges. Using Forman's discrete Morse theory for CW-complexes, we show the first condition can be relaxed to require only that each path between distinct essential vertices is of length at least n-1.

8 pages, 3 figures

References in corpus (1)

• Presentations of Graph Braid Groups

Cited by in corpus (10)

• Presentations of Graph Braid Groups
• Stability phenomena in the homology of tree braid groups
• Geometric presentations of braid groups for particles on a graph
• Discrete Morse functions for graph configuration spaces
• Non-abelian anyons on graphs from presentations of graph braid groups
• Quasi-isometry invariants of weakly special square complexes
• Embeddings of right-angled Artin groups
• Discrete homotopy of token configurations
• Graph of groups decompositions of graph braid groups
• Heisenberg homology of ribbon graphs