Multiplicative structures on cones and duality
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866913201021517824 |
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| author | Cieliebak, Kai Oancea, Alexandru |
| author_facet | Cieliebak, Kai Oancea, Alexandru |
| contents | We initiate the study of multiplicative structures on cones and show that cones of Floer continuation maps fit naturally in this framework. We apply this to give a new description of the multiplicative structure on Rabinowitz Floer homology and cohomology, and to give a new proof of the Poincaré duality theorem which relates the two. The underlying algebraic structure admits two incarnations, both new, which we study and compare: on the one hand the structure of $A_2^+$-algebra on the space $\mathcal{A}$ of Floer chains, and on the other hand the structure of $A_2$-algebra involving $\mathcal{A}$, its dual $\mathcal{A}^\vee$ and a continuation map from $\mathcal{A}^\vee$ to $\mathcal{A}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2008_13165 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Multiplicative structures on cones and duality Cieliebak, Kai Oancea, Alexandru Symplectic Geometry Algebraic Topology 53D40, 55M05, 18N40 We initiate the study of multiplicative structures on cones and show that cones of Floer continuation maps fit naturally in this framework. We apply this to give a new description of the multiplicative structure on Rabinowitz Floer homology and cohomology, and to give a new proof of the Poincaré duality theorem which relates the two. The underlying algebraic structure admits two incarnations, both new, which we study and compare: on the one hand the structure of $A_2^+$-algebra on the space $\mathcal{A}$ of Floer chains, and on the other hand the structure of $A_2$-algebra involving $\mathcal{A}$, its dual $\mathcal{A}^\vee$ and a continuation map from $\mathcal{A}^\vee$ to $\mathcal{A}$. |
| title | Multiplicative structures on cones and duality |
| topic | Symplectic Geometry Algebraic Topology 53D40, 55M05, 18N40 |
| url | https://arxiv.org/abs/2008.13165 |