Braid groups of graphs

Abstract: The braid group of a space \(X\) is the fundamental group of its configuration space, which tracks the motion of some number of particles as they travel through \(X\). When \(X\) is a graph, the configuration space turns out to be a special cube complex, in the sense of Haglund and Wise. I show how these cube complexes are constructed and use graph of groups decompositions to provide methods for computing braid groups of various graphs, as well as criteria for a graph braid group to split as a free product. This has various applications, such as characterising various forms of hyperbolicity in graph braid groups and determining when a graph braid group is isomorphic to a right-angled Artin group.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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