Natural symmetries of secondary Hochschild homology
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866907988479967232 |
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| author | Ayala, David Francis, John Howard, Adam |
| author_facet | Ayala, David Francis, John Howard, Adam |
| contents | We identify the group of framed diffeomorphisms of the torus as a semi-direct product of the torus with the braid group on 3 strands; we also identify the topological monoid of framed local-diffeomorphisms of the torus in similar terms. It follows that the framed mapping class group is this braid group. We show that the group of framed diffeomorphisms of the torus acts on twice-iterated Hochschild homology, and explain how this recovers a host of familiar symmetries. In the case of Cartesian monoidal structures, we show that this action extends to the monoid of framed local-diffeomorphisms of the torus. Based on this, we propose a definition of an unstable secondary cyclotomic structure, and show that iterated Hochschild homology possesses such in the Cartesian monoidal setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_08798 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Natural symmetries of secondary Hochschild homology Ayala, David Francis, John Howard, Adam Algebraic Topology 58D05 We identify the group of framed diffeomorphisms of the torus as a semi-direct product of the torus with the braid group on 3 strands; we also identify the topological monoid of framed local-diffeomorphisms of the torus in similar terms. It follows that the framed mapping class group is this braid group. We show that the group of framed diffeomorphisms of the torus acts on twice-iterated Hochschild homology, and explain how this recovers a host of familiar symmetries. In the case of Cartesian monoidal structures, we show that this action extends to the monoid of framed local-diffeomorphisms of the torus. Based on this, we propose a definition of an unstable secondary cyclotomic structure, and show that iterated Hochschild homology possesses such in the Cartesian monoidal setting. |
| title | Natural symmetries of secondary Hochschild homology |
| topic | Algebraic Topology 58D05 |
| url | https://arxiv.org/abs/2111.08798 |