Symplectic homology and the Eilenberg–Steenrod axioms
| Autor: | Kai Cieliebak, Alexandru Oancea |
|---|---|
| Přispěvatelé: | Universität Augsburg [Augsburg], Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Cieliebak, Kai, Oancea, Alexandru, Albers, Peter |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics 53D40 Eilenberg–Steenrod axioms for a homology theory Homology (mathematics) 01 natural sciences Mathematics::Algebraic Topology Floer homology Rabinowitz–Floer homology Liouville cobordisms Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics Algebraic Topology (math.AT) Mathematics - Algebraic Topology Eilenberg–Steenrod axioms ddc:510 0101 mathematics [MATH]Mathematics [math] Mathematics::Symplectic Geometry 57R17 Axiom Mathematics 53D40 55N40 57R17 57R90 Differential Geometry Exact sequence 010102 general mathematics contact homology Symplectic Geometry 57R90 Mathematics::Geometric Topology [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG] 55N40 Differential Geometry (math.DG) Algebraic Topology Mathematics - Symplectic Geometry [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] symplectic homology [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT] Symplectic Geometry (math.SG) 010307 mathematical physics Geometry and Topology Symplectic geometry |
| Zdroj: | Algebraic and Geometric Topology Algebraic and Geometric Topology, Mathematical Sciences Publishers, 2018, 18 (4), pp.1953-2130. ⟨10.2140/agt.2018.18.1953⟩ Algebr. Geom. Topol. 18, no. 4 (2018), 1953-2130 |
| ISSN: | 1472-2747 1472-2739 |
| DOI: | 10.2140/agt.2018.18.1953⟩ |
| Popis: | 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. Comment: v3: corrected Lemma 7.11. Various other minor modifications and reformatting. Final version to be published in Algebraic and Geometric Topology |
| Databáze: | OpenAIRE |
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