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arXiv · 2512.00454

Orbifold Floer spectral invariants, symmetric product links and Weyl laws

Cheuk Yu Mak·Sobhan Seyfaddini·Ivan Smith
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Abstract

We explain a strategy, based on spectral invariants on symmetric product orbifolds, for proving the smooth closing lemma for Hamiltonian diffeomorphisms of a symplectic manifold when the orbifold quantum cohomologies of its symmetric products possess suitable idempotents. We relate the existence of such idempotents to the manifold containing a sequence of Lagrangian links, whose number of components tends to infinity, satisfying a number of properties. Orbifold Floer cohomology for global quotient orbifolds is used axiomatically, and is constructed in a companion paper. We illustrate this strategy by giving a new proof of the smooth closing lemma for area-preserving diffeomorphisms of the 2-sphere. The construction of suitable Lagrangian links in higher dimensions remains an intriguing open problem.

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Cheuk Yu Mak, Sobhan Seyfaddini, Ivan Smith. 2025-11-29. Orbifold Floer spectral invariants, symmetric product links and Weyl laws. https://arxiv.org/abs/2512.00454

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