Chris McDaniel, University of Massachusetts, Amherst

1-Skeleta, GKM Manifolds, and a Lifting Result

A 1-skeleton in R^n is a finite graph G together with a function that assigns a 1-dimensional subspace of R^n to each edge of G and that satisfies certain compatibility conditions. A GKM T-manifold is a manifold M together with a non-degenerate 2-form w and a compact torus acting "nicely" on the pair (M,w). Following Guillemin and Zara, I will describe both of these objects in greater detail and then explain how to construct a 1-skeleton from a GKM manifold, giving examples along the way. I will then discuss a recent lifting result for 1-skeleta that is related to the problem of extending torus actions on manifolds.

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