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arXiv · 2507.19601

Hamiltonian torus actions and the unimodality of odd Betti numbers

Nicholas Lindsay
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Abstract

This paper is dedicated to the question: Is the sequence of odd Betti numbers of a closed symplectic manifold with a non-trivial Hamiltonian torus action unimodal? Recently, there was some progress on the question for the sequence of even Betti numbers by Cho-Kim and the author. The results of this paper give positive evidence in the case of odd Betti numbers, in dimensions $6,8$ and $10$ under progressively stronger symmetry assumptions.

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Nicholas Lindsay. 2025-07-25. Hamiltonian torus actions and the unimodality of odd Betti numbers. https://arxiv.org/abs/2507.19601

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