**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

### Geometry and Topology Seminar

# 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
Seminar schedule

**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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