Hodge theory of SKT manifolds

Gil R. Cavalcanti

doi:10.1016/j.aim.2020.107270

Hodge theory of SKT manifolds

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We use tools from generalized complex geometry to develop the theory of SKT (a.k.a. pluriclosed Hermitian) manifolds and more generally manifolds with special holonomy with respect to a metric connection with closed skew-symmetric torsion. We develop Hodge theory on such manifolds showing how the reduction of the holonomy group causes a decomposition of the twisted cohomology. For SKT manifolds this decomposition is accompanied by an identity between different Laplacian operators and equates different cohomologies defined in terms of the SKT structure. We illustrate our theory with examples based on Calabi–Eckmann manifolds, instantons, Hopf surfaces and Lie groups.

Original language	English
Article number	107270
Number of pages	42
Journal	Advances in Mathematics
Volume	374
DOIs	https://doi.org/10.1016/j.aim.2020.107270
Publication status	Published - 18 Nov 2020

Funding

Acknowledgments: This research was supported by the Marie Curie Intra European Fellowship PIEF-GA-2008-220178 and the VIDI grant 639.032.221 from NWO, the Dutch science foundation. The author is thankful to Anna Fino, S?nke Rollenske, Ulf Lindstrom, Martin Ro?ek, Stefan Vandoren and Maxim Zabzine for useful conversations.

Keywords

Generalized complex geometry
Generalized Kähler geometry
Hodge theory
Instantons
SKT structure

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10.1016/j.aim.2020.107270

1-s2.0-S0001870820302966-mainFinal published version, 637 KBLicence: CC BY

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Hodge theory of SKT manifolds

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