Piunikhin-Salamon-Schwarz isomorphisms and spectral invariants for conormal bundle

Djuretic, Jovana

doi:10.48550/arxiv.1411.0852

Cited by 2 publications

(2 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The case of the zero section of a cotangent bundle appears in [KM05]. For conormal bundles see [Dju15]. For weakly exact Lagrangians a description of the PSS isomorphism appears in [Lec08] over Z 2 and over arbitrary rings in [HLL11].…”

Section: Relation With Previous Results and Constructionsmentioning

confidence: 99%

The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory

Zapolsky¹

2015

Preprint

View full text Add to dashboard Cite

The purpose of this paper is to extend the construction of the PSS-type isomorphism between the Floer homology and the quantum homology of a monotone Lagrangian submanifold L of a symplectic manifold M , provided that the minimal Maslov number of L is at least two, to arbitrary coefficients. We provide a proof, again over arbitrary coefficients, that this isomorphism respects the natural algebraic structures on both sides, such as the quantum product and the quantum module action. This isomorphism serves as the technical foundation for the construction of Lagrangian spectral invariants in [LZ15]. Our constructions work when the second Stiefel-Whitney class of L vanishes on the image of the boundary homomorphism π3(M, L) → π2(L), a condition strictly weaker than being relatively Pin; in particular we do not require L to be orientable. The constructions are done using canonical orientations, and require no further choices such as relative Pin-structures. Such structures do however play a significant role when endowing the various complexes and homologies with structures of modules over Novikov rings, and in calculations.

show abstract

Section: Relation With Previous Results and Constructionsmentioning

confidence: 99%

The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory

Zapolsky¹

2015

Preprint

View full text Add to dashboard Cite

show abstract

“…In [20], Leclercq constructed spectral invariants for Lagrangian Floer theory in case when L is a closed submanifold of a compact (or convex in infinity) symplectic manifold P and ω| π2(P,L) = 0, µ| π2(P,L) = 0, where µ is Maslov index. Symplectic invariants were further investigated by Eliashberg and Polterovich [11], Polterovich and Rosen [32], Oh [30], Humilière, Leclercq and Seyfaddini [13], by Monzner, Vichery and Zapolsky [26], Lanzat [18] and also in [9], [21,22,23,24]. 1.3.…”

mentioning

confidence: 99%

Spectral invariants in Lagrangian Floer homology of open subset

Katić¹,

Milinković²,

Nikolić³

2017

Differential Geometry and its Applications

View full text Add to dashboard Cite

We define and investigate spectral invariants for Floer homology HF (H, U : M ) of an open subset U ⊂ M in T * M , defined by Kasturirangan and Oh as a direct limit of Floer homologies of approximations. We define a module structure product on HF (H, U : M ) and prove the triangle inequality for invariants with respect to this product. We also prove the continuity of these invariants and compare them with spectral invariants for periodic orbits case in T * M .

show abstract

Piunikhin-Salamon-Schwarz isomorphisms and spectral invariants for conormal bundle

Cited by 2 publications

References 30 publications

The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory

The Lagrangian Floer-quantum-PSS package and canonical orientations in Floer theory

Spectral invariants in Lagrangian Floer homology of open subset

Contact Info

Product

Resources

About