The mapping class group of connect sums of \(S^2 \times S^1\)

Abstract:

Let \(M_n\) denote the connect sum of \(n\) copies of \(S^2 \times S^1\). Laudenbach showed that the mapping class group \(\Mod(M_n)\) is an extension of the group \(\Out(F_n)\) by \((\ZZ/2)^n\), where the latter group is the "sphere twist" subgroup of \(\Mod(M_n)\).

We prove that this extension splits. In this talk, I will describe the splitting and discuss some simplifications of Laudenbach's original proof that arise from our techniques.

This is joint work with N. Broaddus and A. Putman.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | paper | slides )

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

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