Discrete Morse theory and graph braid groups

  title={Discrete Morse theory and graph braid groups},
  author={D. Farley and Lucas Sabalka},
If Γ is any finite graph, then the unlabelled configuration space of n points on Γ, denoted UCnΓ, is the space of n-element subsets of Γ. The braid group of Γ on n strands is the fundamental group of UCnΓ. We apply a discrete version of Morse theory to these UCnΓ, for any n and any Γ, and provide a clear description of the critical cells in every case. As a result, we can calculate a presentation for the braid group of any tree, for any number of strands. We also give a simple proof of a… CONTINUE READING
Highly Cited
This paper has 27 citations. REVIEW CITATIONS


Publications referenced by this paper.
Showing 1-10 of 17 references

Morse theory for cell complexes

  • R Forman
  • Adv. Math. 134 (1998) 90–145 MR1612391 Algebraic…
  • 2005
Highly Influential
9 Excerpts

The geometry of rewriting systems: a proof of the Anick-Groves- Squier theorem

  • K S Brown
  • from: “Algorithms and classification in…
  • 1992
Highly Influential
5 Excerpts

Configuration spaces of colored graphs

  • A Abrams
  • Geom. Dedicata 92
  • 2002

Euler characteristic of the configuration space of a complex

  • Ś R Gal
  • Colloq. Math. 89
  • 2001
2 Excerpts

) [ 3 ] A Abrams , Configuration spaces of colored graphs

  • R Ghrist A Abrams
  • Geom . Dedicata
  • 2000

Configuration spaces of braid groups of graphs

  • A Abrams
  • PhD thesis, UC Berkeley
  • 2000
2 Excerpts

Similar Papers

Loading similar papers…