3 results
Realization of GKM fibrations and new examples of Hamiltonian non-Kähler actions
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- Journal:
- Compositio Mathematica / Volume 159 / Issue 10 / October 2023
- Published online by Cambridge University Press:
- 24 August 2023, pp. 2149-2190
- Print publication:
- October 2023
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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.
Enough vector bundles on orbispaces
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- Journal:
- Compositio Mathematica / Volume 158 / Issue 11 / November 2022
- Published online by Cambridge University Press:
- 28 November 2022, pp. 2046-2081
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- November 2022
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We show that every orbispace satisfying certain mild hypotheses has ‘enough’ vector bundles. It follows that the
$K$-theory of finite rank vector bundles on such orbispaces is a cohomology theory. Global presentation results for smooth orbifolds and derived smooth orbifolds also follow.
POINCARÉ DUALITY FOR K-THEORY OF EQUIVARIANT COMPLEX PROJECTIVE SPACES
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- Journal:
- Glasgow Mathematical Journal / Volume 50 / Issue 1 / January 2008
- Published online by Cambridge University Press:
- 01 January 2008, pp. 111-127
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- January 2008
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