BIRS Workshop Lecture Videos
Topological implications of KÃ¤hler-type symmetries for Hermitian and Almost KÃ¤hler manifolds Wilson, Scott
The symmetries of the Hodge diamond of a KÃ¤hler 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 KÃ¤hler manifolds. Both discussions involve zeroeth order terms that vanish in the KÃ¤hler 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.
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