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Topological implications of Kähler-type symmetries for Hermitian and Almost Kähler manifolds

Banff International Research Station for Mathematical Innovation and Discovery

The symmetries of the Hodge diamond of a Kähler manifold provide many non-trivial conditions on both the Hodge numbers and the Betti numbers of the underlying manifold. In this talk I will describe generalizations of these to the setting of Hermitian and almost Kähler manifolds. Both discussions involve zeroeth order terms that vanish in the Kähler case, and yield an interesting representation of $sl(2)$ on a naturally defined subspace of the harmonic forms. I'll explain several topological corollaries involving Betti numbers and the fundamental group, which is joint work with Joana Cirici. The two discussions have some interesting and yet unexplained algebraic mirror-type symmetry between them, which may lead the participants to interesting questions for future research.

Mathematics; Differential geometry; Algebraic geometry

video/mp4

Author affiliation: Queens College, CUNY

2020-04-29

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74223

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/