Cohomological Lifting of Multi-Toric Graphs

Kael Dixon (), Thomas Bruun Madsen () and Andrew Swann ()
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Kael Dixon: Montreal
Thomas Bruun Madsen: University of West London, School of Computing and Engineering
Andrew Swann: Aarhus University, Department of Mathematics and DIGIT

A chapter in Real and Complex Geometry, 2025, pp 137-158 from Springer

Abstract: Abstract We study G 2 $$ G_{2} $$ -manifolds obtained from circle bundles over symplectic SU ( 3 ) $$ \operatorname {SU}(3) $$ -manifolds with T 2 $$ T^{2} $$ -symmetry. When the geometry is multi-Hamiltonian, we show how the compact part of the resulting multi-moment graph for the G 2 $$ G_{2} $$ -structure may obtained cohomologically from the base. The lifting procedure is illustrated in the context of toric geometry.

Keywords: Holonomy G 2 $$G_2$$; Circle bundle; Torus symmetry; Multi-Hamiltonian geometry; Tri-valent graph; Toric geometry; Primary 53C25; Secondary 14M25, 53C26, 53C29, 53D20 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-92297-8_6

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DOI: 10.1007/978-3-031-92297-8_6

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