S1-Equivariant Symplectic Homology and Linearized Contact Homology
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TLDR
In this paper, it was shown that the positive part of $S^1$-equivariant symplectic homology is isomorphic to linearized contact homology, when the latter is defined.Abstract:
We present three equivalent definitions of $S^1$-equivariant symplectic homology. We show that, using rational coefficients, the positive part of $S^1$-equivariant symplectic homology is isomorphic to linearized contact homology, when the latter is defined. We present several computations and applications, as well as a rigorous definition of cylindrical/linearized contact homology based on an $S^1$-equivariant construction.read more
Citations
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Journal ArticleDOI
Symplectic homology and the Eilenberg–Steenrod axioms
Kai Cieliebak,Alexandru Oancea +1 more
TL;DR: In this paper, the authors give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg-Steenrod axioms except for the dimension axiom.
Journal ArticleDOI
Symplectic capacities from positive $S^1$–equivariant symplectic homology
Jean Gutt,Michael Hutchings +1 more
TL;DR: In this paper, a sequence of symplectic capacities for star-shaped domains in ℝ2n is defined, which are conjecturally equal to the Ekeland-Hofer capacities, but satisfy axioms which allow them to be computed in many more examples.
Journal ArticleDOI
Lusternik–Schnirelmann theory and closed Reeb orbits
TL;DR: In this article, a variant of Lusternik-Schnirelmann theory for the shift operator in equivariant Floer and symplectic homology was developed, and it was shown that the spectral invariants are strictly decreasing under the action of shift operator when periodic orbits are isolated.
Posted Content
Contact manifolds with flexible fillings
TL;DR: In this article, it was shown that all flexible Weinstein fillings of a given contact manifold with vanishing first Chern class have isomorphic integral cohomology; in certain cases, all flexible fillings are symplectomorphic.
Journal ArticleDOI
Symplectic homology and the Eilenberg-Steenrod axioms
Kai Cieliebak,Alexandru Oancea +1 more
TL;DR: In this paper, the authors give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg-Steenrod axioms except for the dimension axiom.
References
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