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arXiv · 2609.06709

Lusternik-Schnirelmann category of Lee Forms on locally conformally symplectic manifolds

Kenji Fukushi
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Abstract

The Lusternik--Schnirelmann category of a closed symplectic manifold admits various estimates. Locally conformally symplectic (LCS) geometry is a generalization of symplectic geometry involving a closed one-form, called the Lee form. In this paper, we introduce Farber's Lusternik--Schnirelmann category for closed one-forms into LCS geometry by applying it to the Lee class. In particular, this provides a new topological approach to LCS structures of the second kind. We then obtain lower bounds for this invariant under LCS blow-ups.

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Kenji Fukushi. 2026-09-06. Lusternik-Schnirelmann category of Lee Forms on locally conformally symplectic manifolds. https://arxiv.org/abs/2609.06709

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