GKM manifolds are not rigid

Goertsches, Oliver; Konstantis, Panagiotis und Zoller, Leopold (2022): GKM manifolds are not rigid. In: Algebraic & Geometric Topology : Agt, Bd. 22, Nr. 7: S. 3511-3532

Abstract

We construct effective GKM T3-actions with connected stabilizers on the total spaces of the two S2-bundles over S6 with identical GKM graphs. This shows that the GKM graph of a simply connected integer GKM manifold with connected stabilizers does not determine its homotopy type. We complement this by a discussion of the minimality of this example: the homotopy type of integer GKM manifolds with con-nected stabilizers is indeed encoded in the GKM graph for smaller dimensions, lower complexity, or lower number of fixed points. Regarding geometric structures on the new example, we find an almost complex structure which is invariant under the action of a subtorus. In addition to the minimal example, we provide an analogous example where the torus actions are Hamiltonian, which disproves symplectic cohomological rigidity for Hamiltonian integer GKM manifolds.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Informatik
• Themengebiete: 000 Informatik, Informationswissenschaft, allgemeine Werke > 004 Informatik
• ISSN: 1472-2739
• Sprache: Englisch