Cohomology of symplectomorphism groups and critical values of Hamiltonians

DOI10.1007/BF01161996zbMath0644.57024OpenAlexW1991149684MaRDI QIDQ1102587

Alan Weinstein

Publication date: 1989

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/174036

zbMATH Keywords

average action integralcritical value of the hamiltonianHamilton's principle of stationary actionintegrals of the symplectic form over integer homology classesloops in the automorphism group of a compact, simply-connected, symplectic manifold

Mathematics Subject Classification ID

Homology and cohomology of Lie groups (57T10) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15) Differential topological aspects of diffeomorphisms (57R50)

Related Items (20)

Action integrals and infinitesimal characters ⋮ Symplectic action around loops in Ham(\(M\)) ⋮ Hamiltonian diffeomorphisms of toric manifolds and flag manifolds ⋮ On the rank of \(\pi_1\)(Ham) ⋮ Quantum integrability and localization formulas ⋮ Invariants of contact structures and transversally oriented foliations ⋮ The diffeology of Milnor's classifying space ⋮ THE NONLINEAR MASLOV INDEX AND THE CALABI HOMOMORPHISM ⋮ The Dixmier-Douady class, the action homomorphism, and group cocycles on the symplectomorphism group ⋮ On a remark by Alan Weinstein ⋮ Localization and diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories ⋮ Generalized symplectic action and symplectomorphism groups of coadjoint orbits ⋮ REMARKS ON INVARIANTS OF HAMILTONIAN LOOPS ⋮ Hamiltonian symplectomorphisms and the Berry phase ⋮ Connections of Berry and Hannay type for moving Lagrangian submanifolds ⋮ Rigid subsets of symplectic manifolds ⋮ Obstruction results in quantization theory ⋮ LIFTING HAMILTONIAN LOOPS TO ISOTOPIES IN FIBRATIONS ⋮ Unnamed Item ⋮ The supersymmetric sigma model, topological quantum mechanics and knot invariants

Cites Work

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• The connection whose holonomy is the classical adiabatic angles of Hannay and Berry and its generalization to the non-integrable case
• Connections of Berry and Hannay type for moving Lagrangian submanifolds
• Pseudo holomorphic curves in symplectic manifolds
• On the variation in the cohomology of the symplectic form of the reduced phase space
• Convexity properties of the moment mapping
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Quantal phase factors accompanying adiabatic changes
• On the Volume Elements on a Manifold
• Diffeomorphisms of the 2-Sphere

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