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Forum Mathematicum

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Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 24, Issue 4


Presentations of graph braid groups

Daniel Farley / Lucas Sabalka
Published Online: 2012-06-29 | DOI: https://doi.org/10.1515/form.2011.086


Let be a graph. The (unlabeled) configuration space of n points on is the space of n-element subsets of . The n-strand braid group of , denoted , is the fundamental group of .

This paper applies the methods of discrete Morse theory to the spaces . We describe how to compute presentations for , where n is an arbitrary natural number and is an arbitrary finite connected graph. Particular attention is paid to the case , and many examples are given.

Keywords: Graph braid group; configuration space; discrete Morse theory

About the article

Received: 2009-08-20

Revised: 2010-03-22

Published Online: 2012-06-29

Published in Print: 2012-07-01

Citation Information: , Volume 24, Issue 4, Pages 827–859, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.086.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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