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arXiv · 2608.26999

On orientability, Poincar\'e duality, and connectivity of GKM graphs

Oliver Goertsches·Panagiotis Konstantis·Leopold Zoller
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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 Poincar\'e 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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Oliver Goertsches, Panagiotis Konstantis, Leopold Zoller. 2026-08-27. On orientability, Poincar\'e duality, and connectivity of GKM graphs. https://arxiv.org/abs/2608.26999

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