Floer theory and reduced cohomology on open manifolds

Groman, Yoel¹

¹ Einstein Institute of Mathematics, The Hebrew University of Jerusalem - Givat Ram, Jerusalem, Israel

Geometry & topology, Tome 27 (2023) no. 4, pp. 1273-1390.

Résumé

We construct Hamiltonian Floer complexes associated to continuous, and even lower semicontinuous, time-dependent exhaustion functions on geometrically bounded symplectic manifolds. We further construct functorial continuation maps associated to monotone homotopies between them, and operations which give rise to a product and unit. The work rests on novel techniques for energy confinement of Floer solutions as well as on methods of non-Archimedean analysis. The definition for general Hamiltonians utilizes the notion of reduced cohomology familiar from Riemannian geometry, and the continuity properties of Floer cohomology. This gives rise, in particular, to local Floer theory. We discuss various functorial properties as well as some applications to existence of periodic orbits and to displaceability.

Détail

DOI : 10.2140/gt.2023.27.1273

Classification : 53D40, 32P05
Keywords: symplectic cohomology, geometrically bounded manifolds, tame symplectic manifolds

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