Uncountably many quasi-isometric torsion-free groups

Vladimir Vankov (Southampton)

20-Jan-2022, 15:05-15:55 (2 years ago)

Abstract: The study of quasi-isometries between finitely generated groups has traditionally been one of the more common questions of geometric group theory, which includes understanding the possible nature of quasi-isometry classes in general. There are several precedents for sets of uncountable cardinality to exhibit surprising behaviour differing from countable sets, especially when it comes to subgroups. We explore generalising constructions of uncountably many torsion groups falling into the same quasi-isometry class via commensurability, to the torsion-free setting. This is done by considering bounded cohomology and appealing to algebraic concepts classically found in finite group theory, in order to produce examples of a continuum of quasi-isometric and torsion-free, but pairwise non-isomorphic finitely generated groups.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( slides )


Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

Organizers: Saul Schleimer*, Robert Kropholler*
*contact for this listing

Export talk to