SMS scnews item created by Boris Lishak at Wed 12 Jun 2019 1429
Type: Seminar
Distribution: World
Calendar1: 18 Jun 2019 1200-1300
CalLoc1: Carslaw 375
CalTitle1: Soroko -- Groups of type FP: their quasi-isometry classes and homological Dehn functions
Auth: borisl@dora.maths.usyd.edu.au

# Groups of type FP: their quasi-isometry classes and homological Dehn functions

### Ignat Soroko (Louisiana State)

June 18, 12:00-13:00 in Carslaw 375

Abstract: There are only countably many isomorphism classes of finitely presented groups, i.e. groups of type $$F_2$$. Considering a homological analog of finite presentability we get the class of groups $$FP_2$$. Ian Leary proved that there are uncountably many isomorphism classes of groups of type $$FP_2$$ (and even of finer class FP). R.Kropholler, Leary and I proved that there are uncountably many classes of groups of type FP even up to quasi-isometries. Since `almost all' of these groups are infinitely presented, the usual Dehn function makes no sense for them, but the homological Dehn function is well-defined. In an on-going project with N.Brady, R.Kropholler and myself, we show that for any integer $$k\ge4$$ there exist uncountably many quasi-isometry classes of groups of type FP with a homological Dehn function $$n^k$$. In this talk I will give the relevant definitions and describe the construction of these groups. Time permitting, I will describe the connection of these groups to the Relation Gap Problem.

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