Realization of GKM fibrations and new examples of Hamiltonian non-Kähler actions

We classify fibrations of abstract $3$-regular GKM graphs over $2$-regular ones, and show that all fibrations satisfying the known necessary conditions for realizability are, in fact, realized as the projectivization of equivariant complex rank-$2$ vector bundles over quasitoric $4$-manifolds or $S^...

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Vydáno v:Compositio mathematica Ročník 159; číslo 10; s. 2149 - 2190
Hlavní autoři: Goertsches, Oliver, Konstantis, Panagiotis, Zoller, Leopold
Médium: Journal Article
Jazyk:angličtina
Vydáno: London, UK London Mathematical Society 01.10.2023
Cambridge University Press
Témata:
Graphs
Hamiltonian functions
Manifolds (mathematics)
Polytopes
X-rays
32Q15
equivariant topology
realization of GKM graphs
55N91
Hamiltonian non-Kähler actions
cohomogeneity one manifolds
53D05
equivariant obstruction theory
GKM fibrations
57R91
equivariant geometric structures
ISSN:0010-437X, 1570-5846
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Shrnutí:We classify fibrations of abstract $3$-regular GKM graphs over $2$-regular ones, and show that all fibrations satisfying the known necessary conditions for realizability are, in fact, realized as the projectivization of equivariant complex rank-$2$ vector bundles over quasitoric $4$-manifolds or $S^4$. We investigate the existence of invariant (stable) almost complex, symplectic, and Kähler structures on the total space. In this way, we obtain infinitely many Kähler manifolds with Hamiltonian non-Kähler actions in dimension $6$ with prescribed one-skeleton, in particular with a prescribed number of isolated fixed points.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X2300742X