Hyperbolicity and $L$-infinity cohomology

Abstract: $L$-infinity cohomology is a quasi-isometry invariant of finitely generated groups. It was introduced by Gersten as a tool to find lower bounds for the Dehn function of some finitely presented groups. I will discuss a generalisation of a theorem of Gersten on surjectivity of the restriction map in $L$-infinity cohomology of groups. This leads to applications on subgroups of hyperbolic groups, quasi-isometric distinction of finitely generated groups and $L$-infinity cohomology calculations for some well-known classes of groups such as RAAGs, Bestvina-Brady groups and $\mathrm{Out}(F_n)$. Along the way, we obtain hyperbolicity criteria for groups of type $FP_2(Q)$ and for those satisfying a rational homological linear isoperimetric inequality.

I will first define L-infinity cohomology and discuss some of its properties. I will then sketch some of the main ideas behind the proofs. This is joint work with Vladimir Vankov.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( paper )

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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 at 13:30. Talks are typically fifty minutes long, with ten minutes for questions.

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