Bounds on spectral norms and barcodes

DOI10.2140/gt.2021.25.3257zbMath1485.57023arXiv1810.09865OpenAlexW4210787036MaRDI QIDQ2078913

Egor Shelukhin, Asaf Kislev

Publication date: 4 March 2022

Published in: Geometry \& Topology (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.09865

zbMATH Keywords

Floer homologyLagrangian submanifoldsspectral normspectral invariantsHamiltonian diffeomorphismsbarcodespersistence modules

Mathematics Subject Classification ID

Symplectic and contact topology in high or arbitrary dimension (57R17) Lagrangian submanifolds; Maslov index (53D12) Symplectic aspects of Floer homology and cohomology (53D40)

Related Items (12)

Families of legendrians and Lagrangians with unbounded spectral norm ⋮ A note on partial quasi-morphisms and products in Lagrangian Floer homology in cotangent bundles ⋮ Another look at the Hofer-Zehnder conjecture ⋮ On the Hofer-Zehnder conjecture ⋮ Viterbo conjecture for Zoll symmetric spaces ⋮ Symplectic embeddings into disk cotangent bundles ⋮ Convergence and Riemannian bounds on Lagrangian submanifolds ⋮ Symplectic cohomology and a conjecture of Viterbo ⋮ Remarks on the oscillation energy of Legendrian isotopies ⋮ Hamiltonian no-torsion ⋮ Approximate identities and Lagrangian Poincaré recurrence ⋮ Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics

Cites Work

• A Lagrangian Piunikhin-Salamon-Schwarz Morphism and Two Comparison Homomorphisms in Floer Homology
• Rational homotopy theory and differential forms
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Categorification of Seidel's representation
• An algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves
• Displacement of polydisks and Lagrangian Floer theory
• Floer trajectories with immersed nodes and scale-dependent gluing
• Floer cohomology and pencils of quadrics
• Partial quasimorphisms and quasistates on cotangent bundles, and symplectic homogenization
• Persistent homology and Floer-Novikov theory
• Observations on the Hofer distance between closed subsets
• Homological Lagrangian monodromy
• A geometric refinement of a theorem of Chekanov
• Disjoinable Lagrangian spheres and dilations
• Symplectic topology as the geometry of generating functions
• On the topology of Lagrangian submanifolds examples and counter-examples
• An open string analogue of Viterbo functoriality
• Stability of persistence diagrams
• Autonomous Hamiltonian flows, Hofer's geometry and persistence modules
• Fukaya categories and Picard-Lefschetz theory
• Spectral invariants in Lagrangian Floer theory
• Sc-smoothness, retractions and new models for smooth spaces
• Hamiltonian dynamics on convex symplectic manifolds
• Rigidity and uniruling for Lagrangian submanifolds
• Lusternik-Schnirelman-theory for Lagrangian intersections
• A quantum cup-length estimate for symplectic fixed points
• Floer homology and Arnold conjecture
• Symplectic topology as the geometry of action functional. II: Pants product and cohomological invariants
• Arnold conjecture and Gromov-Witten invariant
• The Maslov index for paths
• Symplectic packings and algebraic geometry
• \(\pi_1\) of symplectic automorphism groups and invertibles in quantum homology rings
• Rigidity and gluing for Morse and Novikov complexes
• The quantum Euler class and the quantum cohomology of the Grassmannians
• Invariant Finsler metrics on the space of Lagrangian embeddings
• On the action spectrum for closed symplectically aspherical manifolds
• Hamiltonian pseudo-rotations of projective spaces
• Simple homotopy equivalence of nearby Lagrangians
• A quasi-isometric embedding into the group of Hamiltonian diffeomorphisms with Hofer's metric
• Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds
• Computing persistent homology
• Piunikhin-Salamon-Schwarz isomorphisms for Lagrangian intersections
• Chain level Floer theory and Hofer's geometry of the Hamiltonian diffeomorphism group.
• The geometry of symplectic energy
• Topological persistence and simplification
• Symplectic cuts
• On operad structures of moduli spaces and string theory
• Lagrangian intersections, symplectic energy, and areas of holomorphic curves
• The action spectrum and \(C^0\) symplectic topology
• Barcodes and area-preserving homeomorphisms
• Covariantly functorial wrapped Floer theory on Liouville sectors
• Coisotropic Hofer-Zehnder capacities and non-squeezing for relative embeddings
• \(p\)-cyclic persistent homology and Hofer distance
• Coisotropic rigidity and \(C^0\)-symplectic geometry
• Floer trajectories and stabilizing divisors
• Constructing the virtual fundamental class of a Kuranishi atlas
• Gromov-Witten invariants and pseudo symplectic capacities
• Lagrangian skeletons, periodic geodesic flows and symplectic cuttings
• Lagrangian intersections and the Serre spectral sequence
• Lagrangian non-intersections
• Lagrangian circle actions
• Lagrangian cobordism and metric invariants
• Lectures on Geometry
• Combinatorial Floer Homology
• Function Theory on Symplectic Manifolds
• A Beginner’s Introduction to Fukaya Categories
• Induced Matchings and the Algebraic Stability of Persistence Barcodes
• Symplectic displacement energy for Lagrangian submanifolds
• The Structure and Stability of Persistence Modules
• On the topological properties of symplectic maps
• Topological properties of Hamiltonian circle actions
• Spectral numbers in Floer theories
• A relative Seidel morphism and the Albers map
• THE SHARP ENERGY-CAPACITY INEQUALITY
• Topology and data
• Rigid subsets of symplectic manifolds
• Intersection de sous-variétés lagrangiennes, fonctionnelles d'action et indice des systèmes hamiltoniens
• Graded lagrangian submanifolds
• The Lagrangian Cubic Equation
• Spectral invariants for monotone Lagrangians
• Cuplength estimates on lagrangian intersections
• Hofer's metrics and boundary depth
• Khovanov homology from Floer cohomology
• Embeddings of free groups into asymptotic cones of Hamiltonian diffeomorphisms
• Decomposition of pointwise finite-dimensional persistence modules
• Polyfold and Fredholm Theory
• Spectral Invariants with Bulk, Quasi-Morphisms and Lagrangian Floer Theory
• C 0-Limits of Hamiltonian Paths and the Oh–Schwarz Spectral Invariants
• Symplectic Topology and Floer Homology
• Symplectic Topology and Floer Homology
• Symplectic cohomology and Viterbo's theorem
• Floer cohomology of -equivariant Lagrangian branes
• Applications of Polyfold Theory I: The Polyfolds of Gromov–Witten Theory
• PERSISTENCE BARCODES FOR SHAPES
• Barcodes: The persistent topology of data

This page was built for publication: Bounds on spectral norms and barcodes