Another look at the Hofer–Zehnder conjecture

Çineli, Erman; Ginzburg, Viktor L.; Gürel, Başak Z.

doi:10.1007/s11784-022-00937-w

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2023

2024

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Cited by 3 publications

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“…Collier et al gave a proof of the Franks theorem in the case of Ham(CP 1 ) using symplectic tools [CKR + 12]. The higher achievement in proving this conjecture is Shelukhin's theorem showing a homology version of this conjecture in a class of symplectic manifolds including CP d (see [She22] and also [All22a,CGG22]). In this article, we prove an extension of this theorem to the weighted projective spaces.…”

Section: Introductionmentioning

confidence: 99%

On the Hofer–Zehnder conjecture on weighted projective spaces

Allais¹

2023

Compositio Math.

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We prove an extension of the homology version of the Hofer–Zehnder conjecture proved by Shelukhin to the weighted projective spaces which are symplectic orbifolds. In particular, we prove that if the number of fixed points counted with their isotropy order as multiplicity of a non-degenerate Hamiltonian diffeomorphism of such a space is larger than the minimum number possible, then there are infinitely many periodic points.

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Section: Introductionmentioning

confidence: 99%