Homological filling functions and the word problem

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• Robert Kropholler (Warwick)
• Wednesday 18 May 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Henry Wilton.

For finitely generated groups the word problem asks for the existence of an algorithm that takes in words in a finite generating set and decides if a word is trivial or not. For finitely presented groups this is equivalent to the Dehn function being sub-recursive. There is an analogue of the Dehn function for groups of type $FP_2$, this function measures the difficulty of filling loops in a certain space with surfaces. In joint work with Noel Brady and Ignat Soroko, we give computations of the homological filling functions for Ian Leary’s groups $G_L(S)$. We use this to show that there are uncountably many groups with homological filling function $n^4$. This gives groups that have sub-recursive homological filling function but unsolvable word problem.

This talk is part of the Differential Geometry and Topology Seminar series.

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