Group cohomology and quasi-isometries
5th October 2022, 2:30 pm – 3:30 pm
Fry Building, 2.04
We will examine the relationship between extensions of groups and second cohomology. It was an observation of Gersten that cohomology classes which are bounded result in group extensions which have certain geometric properties: namely being quasi-isometric to the trivial extension. We will use this idea, combined with phenomena which only occur at uncountable cardinalities, to construct a continuum of torsion-free groups which are all quasi-isometric to each other, but are pairwise non-isomorphic.