Centralisers and classifying spaces for $\mathrm{Out}(F_N)$

Abstract: In this talk I will outline reduction theory for mapping classes and explain various attempts to construct similar machinery for elements of $\mathrm{Out}(F_N)$. I will then present a new reduction theory for studying centralisers of elements in $\mathrm{IA}_3(N)$, the finite index level three congruence subgroup of $\mathrm{Out}(F_N)$. Using this I will explain an application to the classifying space for virtually cyclic subgroups, a space notable for its appearance in the Farrell--Jones Conjecture.

Based on joint work with Yassine Guerch and Luis Jorge Sanchez Saldana.

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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