scholarly journals Spectral invariants in Lagrangian Floer theory

2008 ◽  
Vol 2 (2) ◽  
pp. 249-286 ◽  
Author(s):  
Rémi Leclercq ◽  
Keyword(s):  
Spectral Invariants ◽  
Floer Theory

scholarly journals DUALITY IN FILTERED FLOER–NOVIKOV COMPLEXES

2010 ◽  
Vol 02 (02) ◽  
pp. 233-258 ◽  
Author(s):  
MICHAEL USHER
Keyword(s):  
Chain Complex ◽  
Bilinear Pairing ◽  
Symplectic Manifolds ◽  
Duality Relation ◽  
Spectral Invariants ◽  
Floer Theory ◽  
Intersection Pairing ◽  
Period Map ◽  
New Formula ◽  
Special Case

We prove that a certain bilinear pairing (analogous to the Poincaré–Lefschetz intersection pairing) between filtered sub- and quotient complexes of a Floer-type chain complex and of its "opposite complex" is always nondegenerate on homology. This implies a duality relation for the Oh–Schwarz-type spectral invariants of these complexes which (in Hamiltonian Floer theory) was established in the special case that the period map has discrete image by Entov and Polterovich. The duality relation served as a key lemma in Entov and Polterovich's construction of a Calabi quasimorphism on certain rational symplectic manifolds, and the result that we prove here implies that their construction remains valid when the rationality hypothesis is dropped. Apart from this, we also use the nondegeneracy of the pairing to establish a new formula for what we have previously called the boundary depth of a Floer chain complex; this formula shows that the boundary depth is unchanged under passing to the opposite complex.

scholarly journals Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory

2019 ◽  
Vol 260 (1254) ◽  
pp. 0-0
Author(s):  
Kenji Fukaya ◽  
Yong-Geun Oh ◽  
Hiroshi Ohta ◽  
Kaoru Ono
Keyword(s):  
Spectral Invariants ◽  
Floer Theory

scholarly journals Comparison of spectral invariants in Lagrangian and Hamiltonian Floer theory

Filomat ◽  
2016 ◽  
Vol 30 (5) ◽  
pp. 1161-1174 ◽  
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.

scholarly journals Spectral invariants for monotone Lagrangians

2018 ◽  
Vol 10 (03) ◽  
pp. 627-700 ◽  
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.

scholarly journals On independence of iterated Whitehead doubles in the knot concordance group

2018 ◽  
Vol 27 (01) ◽  
pp. 1850003
Author(s):  
Kyungbae Park
Keyword(s):  
Correction Term ◽  
Khovanov Homology ◽  
Floer Theory ◽  
Knot Concordance ◽  
Torus Knot ◽  
Linearly Independent ◽  
Heegaard Floer

Let [Formula: see text] be the positively clasped untwisted Whitehead double of a knot [Formula: see text], and [Formula: see text] be the [Formula: see text] torus knot. We show that [Formula: see text] and [Formula: see text] are linearly independent in the smooth knot concordance group [Formula: see text] for each [Formula: see text]. Further, [Formula: see text] and [Formula: see text] generate a [Formula: see text] summand in the subgroup of [Formula: see text] generated by topologically slice knots. We use the concordance invariant [Formula: see text] of Manolescu and Owens, using Heegaard Floer correction term. Interestingly, these results are not easily shown using other concordance invariants such as the [Formula: see text]-invariant of knot Floer theory and the [Formula: see text]-invariant of Khovanov homology. We also determine the infinity version of the knot Floer complex of [Formula: see text] for any [Formula: see text] generalizing a result for [Formula: see text] of Hedden, Kim and Livingston.

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