[Binghamton Geometry Topology Seminar] Seminar This Week

[Matthew R Haulmark]

Hi everyone,

This week our speaker is Ignat Soroko of  Louisiana State University. Links
and details are below.

Zoom link for the seminar, 2:50 - 3:50:
https://binghamton.zoom.us/j/94057178271

Zoom link for the coffee, 12:30 - 1:30:
https://binghamton.zoom.us/j/96674397432
*Title: *Groups of type FP: their quasi-isometry classes and homological
Dehn functions

*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.


See you on Thursday!

Best,

Matt
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