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# Discrete Morse theory and graph braid groups

@inproceedings{Farley2005DiscreteMT, title={Discrete Morse theory and graph braid groups}, author={D. Farley and Lucas Sabalka}, year={2005} }

- Published 2005

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

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