On orientability, Poincaré duality, and connectivity of GKM graphs
Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller
Abstract
We investigate a combinatorial notion of orientability for abstract GKM graphs and its connections to graph cohomology in the sense of Guillemin--Zara. In particular, we prove that orientability of the GKM graph is equivalent to Poincaré duality of the rational (non-equivariant) graph cohomology algebra. As an application, we prove that orientable GKM graphs remain connected after removing any single vertex.
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