University of Cambridge > Talks.cam > Differential Geometry and Topology Seminar > Homological filling functions and the word problem

Homological filling functions and the word problem

Add to your list(s) Download to your calendar using vCal

  • UserRobert Kropholler (Warwick)
  • ClockWednesday 18 May 2022, 16:00-17:00
  • HouseMR13.

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.

Tell a friend about this talk:

This talk is included in these lists:

Note that ex-directory lists are not shown.

 

© 2006-2022 Talks.cam, University of Cambridge. Contact Us | Help and Documentation | Privacy and Publicity