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arXiv · 2509.00392

Extensions of realizable Hamiltonian and complexity one GKM$_4$ graphs

Oliver Goertsches·Grigory Solomadin
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Abstract

We prove that the GKM graphs of GKM$_4$ manifolds that are either Hamiltonian or of complexity one extend to torus graphs. The arguments are based on a reformulation of the extension problem in terms of a natural representation of the fundamental group of the GKM graph, using a coordinate-free version of the axial function group of Kuroki, as well as on covers of GKM graphs and acyclicity results for orbit spaces of GKM manifolds.

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Oliver Goertsches, Grigory Solomadin. 2025-08-30. Extensions of realizable Hamiltonian and complexity one GKM$_4$ graphs. https://arxiv.org/abs/2509.00392

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