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Cohomological Lifting of Multi-Toric Graphs

In: Real and Complex Geometry

Author

Listed:
  • Kael Dixon

    (Montreal)

  • Thomas Bruun Madsen

    (University of West London, School of Computing and Engineering)

  • Andrew Swann

    (Aarhus University, Department of Mathematics and DIGIT)

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.

Suggested Citation

  • Kael Dixon & Thomas Bruun Madsen & Andrew Swann, 2025. "Cohomological Lifting of Multi-Toric Graphs," Springer Books, in: Liviu Ornea (ed.), Real and Complex Geometry, pages 137-158, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-92297-8_6
    DOI: 10.1007/978-3-031-92297-8_6
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