Functors and Computations in Floer homology with Applications Part II

Abstract

The results in this paper concern computations of Floer cohomology using generating functions. The first part proves the isomorphism between Floer cohomology and Generating function cohomology introduced by Lisa Traynor. The second part proves that the Floer cohomology of the cotangent bundle (in the sense of Part I), is isomorphic to the cohomology of the loop space of the base. This has many consequences, some of which were given in Part I (GAFA, Geom. funct. anal. Vol. 9 (1999) 985-1033), others will be given in forthcoming papers. The results in this paper had been announced (with indications of proof) in a talk at the ICM 94 in Z{ü}rich. Up to typos, this is the revised version from 2003.

Version revised in 2003

Cited by in corpus (107)

• Geometry of contact transformations and domains: orderability versus squeezing
• Covariantly functorial wrapped Floer theory on Liouville sectors
• Floer homology and the heat flow
• An exact sequence for contact- and symplectic homology
• Fukaya categories and deformations
• Brieskorn manifolds in contact topology
• Perturbed closed geodesics are periodic orbits: Index and Transversality
• Knot and braid invariants from contact homology II, with an appendix written jointly with Siddhartha Gadgil
• The monotone wrapped Fukaya category and the open-closed string map
• Floer theory for negative line bundles via Gromov-Witten invariants
• Twisted supergravity and its quantization
• Symplectic cohomology and q-intersection numbers
• Symplectic cohomology and Viterbo's theorem
• $S^1$-equivariant symplectic homology and linearized contact homology
• Koszul duality patterns in Floer theory
• Deformations of symplectic cohomology and exact Lagrangians in ALE spaces
• J-holomorphic curves, moment maps, and invariants of Hamiltonian group actions
• Floer theory for Lagrangian cobordisms
• Rabinowitz Floer homology: A survey
• Floer theory and reduced cohomology on open manifolds
• Positive topological entropy of Reeb flows on spherizations
• Noncontractible periodic orbits in cotangent bundles and Floer homology
• A stable infinity-category of Lagrangian cobordisms
• Novikov-symplectic cohomology and exact Lagrangian embeddings
• Symplectic and contact differential graded algebras
• Subcritical Stein manifolds are split
• Contact Homology, Capacity and Non-Squeezing in R^2n x S^1 via Generating Functions
• Floer homology of automorphisms of Liouville domains
• From symplectic cohomology to Lagrangian enumerative geometry
• Exotic symplectic manifolds from Lefschetz fibrations
• Displaceability and the mean Euler characteristic
• Effect of Legendrian Surgery
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Maximal contact and symplectic structures
• A biased view of symplectic cohomology
• Floer homology of cotangent bundles and the loop product
• Spectral invariants with bulk, quasimorphisms and Lagrangian Floer theory
• String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
• Cyclic A_\infty Structures and Deligne's Conjecture
• Squeezing in Floer theory and refined Hofer-Zehnder capacities of sets near symplectic submanifolds
• Continuation homomorphism in Rabinowitz Floer homology for symplectic deformations
• Conormal bundles, contact homology and knot invariants
• Orlov and Viterbo functors in partially wrapped Fukaya categories
• Morse-Conley-Floer Homology
• Floer Cohomology, Multiplicity and the Log Canonical Threshold
• Symplectic Banach-Mazur distances between subsets of C^n
• Periodic Symplectic Cohomologies
• Distinguishing between exotic symplectic structures
• A geometric criterion for generating the Fukaya category
• Polyfolds, Cobordisms, and the strong Weinstein conjecture
• Homological mirror symmetry for Milnor fibers of simple singularities
• Homotopy type of the unitary group of the uniform Roe algebra on ${\mathbb{Z}}^n$
• Floer theory of disjointly supported Hamiltonians on symplectically aspherical manifolds
• On the minimal number of periodic orbits on some hypersurfaces in ${\mathbb{R}}^{2n}$
• Symplectic capacity and short periodic billiard trajectory
• Symplectic deformations of Floer homology and non-contractible periodic orbits in twisted disc bundles
• Contact orderability up to conjugation
• Symplectic homology of convex domains and Clarke's duality
• Gromov-Witten invariants and pseudo symplectic capacities
• Remarks on symplectic capacities of $p$-products
• Open books for Boothby-Wang bundles, fibered Dehn twists and the mean Euler characteristic
• Hofer-Zehnder capacity and a Hamiltonian circle action with noncontractible orbits
• Propagation in Hamiltonian dynamics and relative symplectic homology
• On periodic points of Hamiltonian diffeomorphisms of $\mathbb{C}{\text{P}}^d$ via generating functions
• Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
• Loop coproduct in Morse and Floer homology
• Local Floer homology and infinitely many simple Reeb orbits
• A spectral sequence for symplectic homology
• Equivariant symplectic homology and multiple closed Reeb orbits
• Monodromy of monomially admissible Fukaya-Seidel categories mirror to toric varieties
• Symplectic homology of disc cotangent bundles of domains in Euclidean space
• Poincaré duality for loop spaces
• On the complement of a positive normal crossing divisor with no triple intersection in a projective variety
• Persistence modules, symplectic Banach-Mazur distance and Riemannian metrics
• Viterbo's transfer morphism for symplectomorphisms
• Disjoinable Lagrangian tori and semisimple symplectic cohomology
• Mirror symmetry for the Tate curve via tropical and log corals
• Floer cohomology and pencils of quadrics
• Versality in mirror symmetry
• Spectral spread and non-autonomous Hamiltonian diffeomorphisms
• Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem
• The sharp energy-capacity inequality on convex symplectic manifolds
• Exact Calabi-Yau categories and odd-dimensional Lagrangian spheres
• Time-periodic solutions of Hamiltonian PDEs using pseudoholomorphic curves
• Hofer-Zehnder capacity and Hamiltonian circle actions
• The equivariant pair-of-pants product in fixed point Floer cohomology
• Morse theory on the loop space of flat tori and symplectic Floer theory
• The Maslov class of Lagrangian tori and quantum products in Floer cohomology
• Legendrian contact homology for attaching links in higher dimensional subcritical Weinstein manifolds
• An intertwining relation for equivariant Seidel maps
• On the minimal symplectic area of Lagrangians
• Hofer-Zehnder capacity of unit disk cotangent bundles and the loop product
• The role of the Legendre transform in the study of the Floer complex of cotangent bundles
• Fibered Symplectic Cohomology and the Leray-Serre Spectral Sequence
• Finiteness of ${\pi }_1$-sensitive Hofer-Zehnder capacity and equivariant loop space homology
• Spectrum estimates of Hill's lunar problem
• A survey on the Theorem of Chekhanov
• An obstruction to conservation of volume in contact dynamics
• Categorical non-properness in wrapped Floer theory
• Symplectic homology of displaceable Liouville domains and Leafwise intersection points
• Stein domains with exotic contact boundaries
• A note on the representability of a certain Hamiltonian capacity
• Chen-Ruan Cohomology of cotangent orbifolds and Chas-Sullivan String Topology
• Equivariant symplectic homology of Anosov contact structures
• Symplectic rigidity, symplectic fixed points and global perturbations of Hamiltonian systems
• Orbifold String Topology
• Partitions of the set of natural numbers and symplectic homology