GKM theory and Hamiltonian non-Kähler actions in dimension 6

2019/03/27 by Goertsches, Oliver, Konstantis, Panagiotis, Zoller, Leopold · 1 citation
#Algebraic Topology (math.AT) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1903.11684

Abstract

Using the classification of 6-dimensional manifolds by Wall, Jupp and Žubr, we observe that the diffeomorphism type of simply-connected, compact 6-dimensional integer GKM T²-manifolds is encoded in their GKM graph. As an application, we show that the 6-dimensional manifolds on which Tolman and Woodward constructed Hamiltonian, non-Kähler T²-actions with finite fixed point set are both diffeomorphic to Eschenburg's twisted flag manifold SU(3)//T². In particular, they admit a noninvariant Kähler structure.

Cited by

• On Hopf's conjecture and positive second intermediate Ricci curvature

Related

• Realization of GKM fibrations and new examples of Hamiltonian non-Kähler actions
• Monotone Symplectic Six-Manifolds that admit a Hamiltonian GKM Action are diffeomorphic to Smooth Fano Threefolds
• On the Stiefel-Whitney classes of GKM manifolds
• Hard Lefschetz Property for Hamiltonian torus actions on 6-dimensional GKM manifolds
• GKM theory for torus actions with non-isolated fixed points