Pseudo-rotations and Steenrod squares

DOI10.3934/jmd.2020010zbMath1466.53094arXiv1905.05108OpenAlexW3095461184MaRDI QIDQ2025338

Egor Shelukhin

Publication date: 12 May 2021

Published in: Journal of Modern Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.05108

zbMATH Keywords

Hamiltonian diffeomorphismpseudo-rotationequivariant pair-of-pants productquantum Steenrod square

Mathematics Subject Classification ID

Symplectic aspects of Floer homology and cohomology (53D40) Steenrod algebra (55S10) Symplectic and canonical mappings (37J11) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

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Cites Work

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• Persistent homology and Floer-Novikov theory
• Local Floer homology and infinitely many simple Reeb orbits
• Local Floer homology and the action gap
• Action and index spectra and periodic orbits in Hamiltonian dynamics
• Hamiltonian \(S^1\)-manifolds are uniruled
• Rigidity and uniruling for Lagrangian submanifolds
• Arnold conjecture and Gromov-Witten invariant
• Hamiltonian pseudo-rotations of projective spaces
• A construction of the quantum Steenrod squares and their algebraic relations
• Pseudo-rotations and Steenrod squares revisited
• Pseudo-rotations and holomorphic curves
• Pseudo-rotations with sufficiently Liouvillean rotation number are \(C^0\)-rigid
• Hamiltonian \(S^1\)-spaces with large equivariant pseudo-index
• Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves
• The equivariant pair-of-pants product in fixed point Floer cohomology
• 12, 24 and beyond
• Hyperbolic fixed points and periodic orbits of Hamiltonian diffeomorphisms
• Morse theory for periodic solutions of hamiltonian systems and the maslov index
• On the iterated Hamiltonian Floer homology
• Conley Conjecture Revisited
• Symplectic Topology and Floer Homology
• On the Chern numbers and the Hilbert polynomial of an almost complex manifold with a circle action
• Constructions in elliptic dynamics