Barcodes and area-preserving homeomorphisms

DOI10.2140/gt.2021.25.2713zbMath1494.37040arXiv1810.03139OpenAlexW4206269420MaRDI QIDQ2058825

Sobhan Seyfaddini, Frédéric Le Roux, Claude Viterbo

Publication date: 10 December 2021

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

Full work available at URL: https://arxiv.org/abs/1810.03139

zbMATH Keywords

barcodetopological dynamicssymplectic topologyarea-preserving homeomorphisms

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Symplectic aspects of Floer homology and cohomology (53D40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39)

Related Items (9)

Quantitative Heegaard Floer cohomology and the Calabi invariant ⋮ On the Hofer-Zehnder conjecture ⋮ Viterbo conjecture for Zoll symmetric spaces ⋮ Symplectic cohomology and a conjecture of Viterbo ⋮ Barcodes as summary of loss function topology ⋮ Proof of the simplicity conjecture ⋮ Hypoelliptic operators in geometry. Abstracts from the workshop held May 21--26, 2023 ⋮ Bounds on spectral norms and barcodes ⋮ Persistence modules, symplectic Banach–Mazur distance and Riemannian metrics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spectral killers and Poisson bracket invariants
• Persistent homology and Floer-Novikov theory
• On the structure of homeomorphisms of the open annulus
• The Conley conjecture
• Local Floer homology and the action gap
• Subharmonic solutions of Hamiltonian equations on tori
• Points fixes d'une application symplectique homologue à l'identité
• Symplectic topology as the geometry of generating functions
• An equivariant foliated version of Brouwer's translation theorem
• Action and index spectra and periodic orbits in Hamiltonian dynamics
• Pseudo-rotations of the open annulus
• Stability of persistence diagrams
• Autonomous Hamiltonian flows, Hofer's geometry and persistence modules
• Persistance d'intersection avec la section nulle au cours d'une isotopie hamiltonienne dans un fibré cotangent
• Lusternik-Schnirelman-theory for Lagrangian intersections
• Witten's complex and infinite dimensional Morse theory
• L'espace des homéomorphismes du plan qui admettent un seul point fixe d'indice donné est connexe par arcs
• A bound for the fixed-point index of an area-preserving map with applications to mechanics
• A dynamical property of homeomorphisms of the plane in the neighborhood of a fixed point of index \(>1\)
• An index theorem for the homeomorphisms of the plane near a fixed point
• Computing persistent homology
• Symplectic fixed points and holomorphic spheres
• The geometry of symplectic energy
• Precise Arrhenius law for \(p\)-forms: the Witten Laplacian and Morse-Barannikov complex
• Simplicity of homeo\((\mathbb{D}^2,\partial\mathbb{D}^2\), Area) and fragmentation of symplectic diffeomorphisms
• Rigidity of mapping class group actions on \(S^1\)
• The action spectrum and \(C^0\) symplectic topology
• Persistent homology and microlocal sheaf theory
• The group of Hamiltonian homeomorphisms and \(C^0\)-symplectic topology
• Fourier integral operators. I
• Measure-preserving homeomorphisms and metrical transitivity
• The topological Rohlin property and topological entropy
• On Continuity of Quasimorphisms for Symplectic Maps
• The Structure and Stability of Persistence Modules
• On the Hopf Index and the Conley Index
• THE SHARP ENERGY-CAPACITY INEQUALITY
• Pourquoi les points périodiques des homéomorphismes du plan tournent-ils autour de certains points fixes ?
• A bound for the fixed point index of area-preserving homeomorphisms of two-manifolds
• Structure of the group of homeomorphisms preserving a good measure on a compact manifold
• Removing Index 0 Fixed Points for Area Preserving Maps of Two-Manifolds
• A COMPARISON OF HOFER'S METRICS ON HAMILTONIAN DIFFEOMORPHISMS AND LAGRANGIAN SUBMANIFOLDS
• The local rotation set is an interval
• Dynamique des homéomorphismes du plan au voisinage d'un point fixe
• Cuplength estimates on lagrangian intersections
• Topological Persistence in Geometry and Analysis
• C 0-Limits of Hamiltonian Paths and the Oh–Schwarz Spectral Invariants
• Commutators and diffeomorphisms of surfaces
• Proximity of persistence modules and their diagrams
• Topological groups with Rokhlin properties
• A dynamical property for planar homeomorphisms and an application to the problem of canonical position around an isolated fixed point

This page was built for publication: Barcodes and area-preserving homeomorphisms