On torus equivariant $S^4$-bundles over $S^4$ and Petrie-type Questions for GKM Manifolds

Abstract: In GKM theory one associates to certain torus actions on closed manifolds a labelled graph which describes the induced action on the equivariant one-skeleton. It can be regarded as a generalization of (quasi)toric theory, retaining only the one-skeleton of the orbit space polytope. In this talk I will explain an interesting class of examples of GKM manifolds in dimension 8 with exotic behavior: it contains pairs of homotopy equivalent GKM manifolds with different first Pontryagin class, as well as pairs of GKM actions on the same smooth manifold whose GKM graphs do not agree as unsigned graphs. This is in line with previous results that show that GKM manifolds exhibit rigid behaviour only in dimensions up to 6.

This is joint work with Panagiotis Konstantis and Leopold Zoller.

algebraic topologydifferential geometrygeometric topology

Audience: researchers in the topic

Virtual seminar on geometry with symmetries

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

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