Gauged Floer Homology and Spectral Invariants

We give a construction of the Piunikhin-Salamon-Schwarz isomorphism between the Morse homology and the Floer homology generated by Hamiltonian orbits starting at the zero section and ending at the conormal bundle. We also prove that this isomorphism is natural in the sense that it commutes with the isomorphisms between the Morse homology for different choices of the Morse function and the Floer homology for different choices of the Hamiltonian. We define a product on the Floer homology and prove triangle inequality for conormal spectral invariants with respect to this product.

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Spectral invariants in Rabinowitz-Floer homology and global Hamiltonian perturbations

Journal of Modern Dynamics ◽

10.3934/jmd.2010.4.329 ◽

2010 ◽

Vol 4 (2) ◽

pp. 329-357 ◽

Cited By ~ 17

Author(s):

Peter Albers ◽

◽

Urs Frauenfelder ◽

Keyword(s):

Floer Homology ◽

Spectral Invariants ◽

Rabinowitz Floer Homology

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Comparison of spectral invariants in Lagrangian and Hamiltonian Floer theory

Filomat ◽

10.2298/fil1605161d ◽

2016 ◽

Vol 30 (5) ◽

pp. 1161-1174 ◽

Cited By ~ 2

Author(s):

Jovana Djuretic ◽

Jelena Katic ◽

Darko Milinkovic

Keyword(s):

Periodic Orbits ◽

Symplectic Manifold ◽

Floer Homology ◽

Lagrangian Submanifolds ◽

Spectral Invariants ◽

Floer Theory

We compare spectral invariants in periodic orbits and Lagrangian Floer homology case, for a closed symplectic manifold P and its closed Lagrangian submanifolds L, when ?|?2(P,L)=0, and ?|?2(P,L)=0. We define a product HF*(H)?HF*(H:L) ? HF*(H:L) and prove subadditivity of invariants with respect to this product.

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Spectral invariants for monotone Lagrangians

Journal of Topology and Analysis ◽

10.1142/s1793525318500267 ◽

2018 ◽

Vol 10 (03) ◽

pp. 627-700 ◽

Cited By ~ 3

Author(s):

Rémi Leclercq ◽

Frol Zapolsky

Keyword(s):

Generating Functions ◽

Floer Homology ◽

Spectral Invariants ◽

Seminal Paper ◽

Floer Theory ◽

Cotangent Bundles

Since spectral invariants were introduced in cotangent bundles via generating functions by Viterbo in the seminal paper [73], they have been defined in various contexts, mainly via Floer homology theories, and then used in a great variety of applications. In this paper we extend their definition to monotone Lagrangians, which is so far the most general case for which a “classical” Floer theory has been developed. Then, we gather and prove the properties satisfied by these invariants, and which are crucial for their applications. Finally, as a demonstration, we apply these new invariants to symplectic rigidity of some specific monotone Lagrangians.

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Spectral invariants of distance functions

Journal of Topology and Analysis ◽

10.1142/s1793525316500254 ◽

2016 ◽

Vol 08 (04) ◽

pp. 655-676 ◽

Cited By ~ 2

Author(s):

Suguru Ishikawa

Keyword(s):

Symplectic Manifold ◽

Symplectic Form ◽

Floer Homology ◽

Symplectic Manifolds ◽

Distance Functions ◽

Spectral Invariants ◽

Euclidian Space ◽

Closed Riemann Surface ◽

Genus Formula ◽

Spectral Invariant

Calculating the spectral invariant of Floer homology of the distance function, we can find new superheavy subsets in symplectic manifolds. We show if convex open subsets in Euclidian space with the standard symplectic form are disjointly embedded in a spherically negative monotone closed symplectic manifold, their complement is superheavy. In particular, the [Formula: see text] bouquet in a closed Riemann surface with genus [Formula: see text] is superheavy. We also prove some analogous properties of a monotone closed symplectic manifold. These can be used to extend Seyfaddni’s result about lower bounds of Poisson bracket invariant.

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