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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2203.04465 |
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| _version_ | 1866909093999935488 |
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| author | Wang, Yi |
| author_facet | Wang, Yi |
| contents | Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain level refinement of the gravity algebra structure on the (negative) $S^1$-equivariant homology of the free loop space of a closed oriented smooth manifold, based on work of Irie on chain level string topology and work of Ward on an $S^1$-equivariant version of operadic Deligne's conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_04465 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A cocyclic construction of $S^1$-equivariant homology and application to string topology Wang, Yi Algebraic Topology 55P50, Secondary 19D55, 55N91, 18M85 Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain level refinement of the gravity algebra structure on the (negative) $S^1$-equivariant homology of the free loop space of a closed oriented smooth manifold, based on work of Irie on chain level string topology and work of Ward on an $S^1$-equivariant version of operadic Deligne's conjecture. |
| title | A cocyclic construction of $S^1$-equivariant homology and application to string topology |
| topic | Algebraic Topology 55P50, Secondary 19D55, 55N91, 18M85 |
| url | https://arxiv.org/abs/2203.04465 |