Viterbo’s transfer morphism for symplectomorphisms

Uljarevic, Igor

doi:10.1142/s1793525319500079

Cited by 3 publications

(2 citation statements)

References 19 publications

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“…In the forthcoming work [18], we will confirm that, under certain conditions on the Reeb flow, ⌈c(a, ϕ)⌉ is indeed conjugate invariant, which leads to the notation of a contact capacity of a subset U ⊂ M . For applications, we aim to recover the contact non-squeezing phenomenon in [38] in a concise way.…”

Section: Then For Any Contact Hamiltoniansmentioning

confidence: 99%

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Hamiltonian perturbations in contact Floer homology

Uljarevic

Zhang

2022

J. Fixed Point Theory Appl.

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Based on the contact Hamiltonian Floer theory established in [23] that applies to any (admissible) contact Hamiltonian system (M, ξ = ker α, h), where h is a contact Hamiltonian function on a Liouville fillable contact manifold (M, ξ = ker α), we associate a persistence module to (M, ξ, h), called a gapped module, that is parametrized only by a partially ordered set. It enables us to define various numerical Floer-theoretic invariants. In this paper, we focus on the contact spectral invariants and their applications. Several key properties are proved, which include stability with respect to the Shelukhin-Hofer norm in [37] and a triangle inequality of the contact spectral invariant. In particular, our stability property does not involve any conformal factors; our triangle inequality is derived from a novel analysis on pair-of-pants in the contact Hamiltonian Floer homology. While this paper was nearing completion, the authors were made aware of upcoming work [12], where a similar persistence module for a contact Hamiltonian dynamics was constructed.

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Section: Then For Any Contact Hamiltoniansmentioning

confidence: 99%

“…Zigzag isomorphism. Recall that for any s-smooth family of admissible contact Hamiltonians h s : [0, 1] × M → R for s ∈ [0, 1], in [38], one can construct an isomorphism B({h s } s∈[0,1] ) : HF * (h 0 ) → HF * (h 1 ).…”

Section: Descended Definitionsmentioning

confidence: 99%

Hamiltonian perturbations in contact Floer homology

Uljarevic

Zhang

2022

J. Fixed Point Theory Appl.

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Exotic symplectomorphisms and contact circle actions

Drobnjak

Uljarevic

2021

Commun. Contemp. Math.

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Using Floer-theoretic methods, we prove that the non-existence of an exotic symplectomorphism on the standard symplectic ball, [Formula: see text] implies a rather strict topological condition on the free contact circle actions on the standard contact sphere, [Formula: see text] We also prove an analogue for a Liouville domain and contact circle actions on its boundary. Applications include results concerning the symplectic mapping class group and the fundamental group of the group of contactomorphisms.

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Persistence modules, symplectic Banach-Mazur distance and Riemannian metrics

Stojisavljević

Zhang

2018

Preprint

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Viterbo’s transfer morphism for symplectomorphisms

Cited by 3 publications

References 19 publications

Hamiltonian perturbations in contact Floer homology

Hamiltonian perturbations in contact Floer homology

Exotic symplectomorphisms and contact circle actions

Persistence modules, symplectic Banach-Mazur distance and Riemannian metrics

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