Torus actions with connected isotropy groups

Abstract: Recent work with Michael Wiemeler and Burkhard Wilking analyzes torus representations all of whose isotropy groups are connected. An important structure result is a splitting theorem, which states that the representation splits as a product after passing to the induced action on a suitable fixed-point set. More recently, we found a connection between these representations and combinatorial objects called regular matroids, and we applied work of Seymour to classify torus representations with connected isotropy groups. As an application, we prove new obstructions to the existence of Riemannian metrics with positive sectional curvature and large symmetry. In some cases, the assumption on the torus rank is independent of the manifold dimension.

differential geometrygeometric topology

Audience: researchers in the topic

( paper | video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Differential geometry.

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