A survey of Floer homology for manifolds with contact type boundary or symplectic homology

By A. Oancea. Ensaios matemáticos, 2004

75 citations recorded by the source corpus.

The purpose of this paper is to give a survey of the various versions of Floer homology for manifolds with contact type boundary that have so far appeared in the literature. Under the name of ``Symplectic homology'' or ``Floer homology for manifolds with boundary'' they bear in fact common features and we shall try to underline the principles that unite them. Once this will be accomplished we shall proceed to describe the peculiarity of each of the constructions and the specific applications that unfold out of it: classification of ellipsoids and polydiscs in $\mathbb{C}^n$, stability of the action spectrum for contact type boundaries of symplectic manifolds, existence of closed characteristics on contact type hypersurfaces and obstructions to exact Lagrange embeddings. The computation of the Floer cohomology for balls in $\mathbb{C}^n$ is carried by explicitly perturbing the nondegenerate Morse-Bott spheres of closed characteristics.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2ef04399d51ecfa056c99b454d576fc93ea78336

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Citations in the corpus

Rabinowitz Floer homology and symplectic homology (2009, background): “The 1-periodic orbits of such a Hamiltonian are contained in a compact set and, if the almost complex structure is invariant under homotheties at infinity, solutions of (7) are also contained in a compact set [15, 25].”
Brieskorn manifolds in contact topology (2013, background): “Theorem 5.19 (Espina, Bourgeois–Oancea).”
An open string analogue of Viterbo functoriality (2007, background): “It turns out that these points are actually not boundary points, essentially due the convexity of ∂M (see Section 7d for a proof; alternatively one could use the maximum principle, as in [25] or [21]).”
Symplectic homology as Hochschild homology (2006, unknown): “ar X iv :m at h/ 06 09 03 7v 4 [ m at h. SG ] 9 A pr 2 00 8 SYMPLECTIC HOMOLOGY AS HOCHSCHILD HOMOLOGY PAUL SEIDEL”
Symplectic homology, autonomous Hamiltonians, and Morse-Bott moduli spaces (2007, background): “Regular admissible homotopies of almost complex structures form again a set of the second category in the space of admissible homotopies and the rigid behaviour of H for t ≥ t0, together with the condition ∂sH ≥ 0, ensures again that solutions of (15) and (16) stay in a compact set (see [22]).”
A biased view of symplectic cohomology (2007, unknown): “20 55 v6 [ m at h. SG ] 1 5 Fe b 20 10”
Altering symplectic manifolds by homologous recombination (2010, background): “Besides the original papers [58, 57], a few references are [12, 42, 50, 7, 15, 45].”
The action spectrum and $$C^0$$ symplectic topology (2018, background): “Computation of this type of Floer homology groups is a classical example which can be found in, for example, [5, 36, 52].”
Symplectic cohomology and Viterbo's theorem (2013, methodology): “between different versions of Floer cohomology is performed by Oancea in [57], and for a different class of Hamiltonians by Seidel in [76].”
Symplectic Cohomology and q-Intersection Numbers (2010, background): “The original reference is [43], see also [11] for a different approach; more recent surveys are [28, 36].”