Lectures on Floer homology

By Dietmar Salamon. 2006

317 citations recorded by the source corpus.

Subfields: Computational Mechanics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f425f28539ee1b9777b03e460dba98b246b349ef

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In Computational Mechanics

In Geometry and Topology

Citations in the corpus

THE SHARP ENERGY-CAPACITY INEQUALITY (2008, methodology): “Formally, one obtains the differential on CF∗(H) by counting negative gradient flow lines for AH ; see [23] for a survey of the details of the construction for a large family of symplectic manifolds, and [5],[12] for the general case.”
The monotone wrapped Fukaya category and the open-closed string map (2012, background): “We refer to Salamon [29] for a precise definition of the Floer cohomologyHF ∗(HB) for a HamiltonianHB : B → R defined on a closed monotone symplectic manifold (B,ωB).”
Action and index spectra and periodic orbits in Hamiltonian dynamics (2008, methodology): “(When ¯ x is a k-periodic orbit of a k-periodic Hamiltonian H, the augmented action is defined in a similar fashion.) This definition is inspired by considerations i n [Sa, Section 1.6] and [EP2, Section 1.4], where the Conley–Zehnder index is utilized in place of the mean index.”
Floer theory for negative line bundles via Gromov–Witten invariants (2011, background): “Our conventions differ from [23] by reversing the sign of H, but our index μH in fact agrees with the μH of [23].”
The Weinstein conjecture and theorems of nearby and almost existence (2003, background): “groups are canonically isomorphic, [Fl1, Fl2], see also [PSS, Sa , Sc1].”
A FLOER HOMOLOGY FOR EXACT CONTACT EMBEDDINGS (2007, methodology): “We assume that the reader is familiar with the constructions in Floer theory which can be found in Floer’s original papers [14, 15, 16, 17, 18] or in Salamon’s lectures [42].”
A Lagrangian Piunikhin-Salamon-Schwarz Morphism and Two Comparison Homomorphisms in Floer Homology (2005, background): “A very nice account with many details of Hamiltonian Floer homology for monotone symplectic manifolds can be found in [20].”
Contact homology and homotopy groups of the space of contact structures (2004, background): “It is well-known (see for example [15]) that such an operator is an isomorphism.”
Periodic Orbits of Twisted Geodesic Flows and The Weinstein-Moser Theorem (2007, methodology): “F and J; see [Fl5] and also, e.g., [BPS, Gi9, HS, McSa, Poz, Sa , SZ].”
Rabinowitz Floer homology and symplectic homology (2009, methodology): “Then CZ(x; τ) is the Maslov index of the path Φt as defined in [17, 18].”
On the Floer homology of cotangent bundles (2004, background): “4 in [27] to deal with the case r > 2, see also [31]):”