Orbifold Floer spectral invariants, symmetric product links and Weyl laws

Fuente: arXiv
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Auteurs principaux: Mak, Cheuk Yu, Seyfaddini, Sobhan, Smith, Ivan
Format: Preprint
Publié: 2025
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author Mak, Cheuk Yu
Seyfaddini, Sobhan
Smith, Ivan
author_facet Mak, Cheuk Yu
Seyfaddini, Sobhan
Smith, Ivan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_00454
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Orbifold Floer spectral invariants, symmetric product links and Weyl laws
Mak, Cheuk Yu
Seyfaddini, Sobhan
Smith, Ivan
Symplectic Geometry
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.
title Orbifold Floer spectral invariants, symmetric product links and Weyl laws
topic Symplectic Geometry
url https://arxiv.org/abs/2512.00454