Abrams's stable equivalence for graph braid groups

Paul Prue, Travis Scrimshaw

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In his PhD thesis [1], Abrams proved that, for a natural number n and a graph G with at least n vertices, the n-strand configuration space of G, denoted Cn(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.

Original languageEnglish (US)
Pages (from-to)136-145
Number of pages10
JournalTopology and its Applications
Volume178
DOIs
StatePublished - Sep 30 2014

Bibliographical note

Publisher Copyright:
© 2014 Elsevier B.V.

Keywords

  • Configuration space
  • Discrete Morse theory
  • Graph braid group

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