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2018 Symplectic homology and the Eilenberg–Steenrod axioms
Kai Cieliebak, Alexandru Oancea
Algebr. Geom. Topol. 18(4): 1953-2130 (2018). DOI: 10.2140/agt.2018.18.1953

Abstract

We 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. The resulting long exact sequence of a pair generalizes various earlier long exact sequences such as the handle attaching sequence, the Legendrian duality sequence, and the exact sequence relating symplectic homology and Rabinowitz Floer homology. New consequences of this framework include a Mayer–Vietoris exact sequence for symplectic homology, invariance of Rabinowitz Floer homology under subcritical handle attachment, and a new product on Rabinowitz Floer homology unifying the pair-of-pants product on symplectic homology with a secondary coproduct on positive symplectic homology.

In the appendix, joint with Peter Albers, we discuss obstructions to the existence of certain Liouville cobordisms.

Citation

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Kai Cieliebak. Alexandru Oancea. "Symplectic homology and the Eilenberg–Steenrod axioms." Algebr. Geom. Topol. 18 (4) 1953 - 2130, 2018. https://doi.org/10.2140/agt.2018.18.1953

Information

Received: 28 June 2016; Revised: 9 February 2018; Accepted: 21 February 2018; Published: 2018
First available in Project Euclid: 3 May 2018

zbMATH: 06867653
MathSciNet: MR3797062
Digital Object Identifier: 10.2140/agt.2018.18.1953

Subjects:
Primary: 53D40, 55N40, 57R17
Secondary: 57R90

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 4 • 2018
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