Session S23 - Group actions in Differential Geometry

Friday, July 23, 19:00 ~ 19:30 UTC-3

Torus representations with connected isotropy groups: Structural results and applications

Lee Kennard

Syracuse University, U.S.A.   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

I will discuss recent joint work with Michael Wiemeler and Burkhard Wilking on the topology of manifolds admitting torus-invariant Riemannian metrics with positive sectional curvature. I will focus on one elementary but important part of our proofs, an analysis of the structure of representations of tori with the property that all isotropy groups are connected. Such representations arise any time a compact Riemannian manifold has an isometry group of positive dimension. Our analysis includes a splitting theorem and estimates on the minimum codimension of fixed point sets. More recently, we have observed that these torus representations give rise to totally unimodular matrices and hence provide yet another instance of abstract objects called regular matroids occuring in nature.

Joint work with Michael Wiemeler (University of Muenster) and Burkhard Wilking (University of Muenster).

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