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<p>We prove that the GKM graphs of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\hbox {GKM}_4\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>GKM</mtext> <mn>4</mn> </msub> </math></EquationSource> </InlineEquation> 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.</p>

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Extensions of realizable Hamiltonian and complexity one \(\hbox {GKM}_4\) graphs

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月15日

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  • Oliver Goertsches,
  • Grigory Solomadin

摘要

We prove that the GKM graphs of \(\hbox {GKM}_4\) 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.