Equivariant Heegaard genus of reducible three-manifolds

Abstract:

Suppose that \(M\) is a closed, connected, oriented three-manifold which comes with a group action by a finite group of (orientation preserving) diffeomorphisms. The equivariant Heegaard genus of \(M\) is then the minimal genus of an equivariant Heegaard surface. The equivariant sphere theorem, together with recent work of Scharlemann, suggests that equivariant Heegaard genus might be additive under equivariant connected sum, while analogies with tunnel number suggest it should not be.

I will describe some examples showing that equivariant Heegaard genus can be sub-additive, additive, or super-additive. Building on recent work with Tomova, I’ll sketch machinery that gives rise both to sharp bounds on the addivity of equivariant Heegaard genus and to a closely related invariant that is in fact additive.

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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