Reflexive homology and involutive Hochschild homology as equivariant Loday constructions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911372924682240 |
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| author | Lindenstrauss, Ayelet Richter, Birgit |
| author_facet | Lindenstrauss, Ayelet Richter, Birgit |
| contents | For associative rings with anti-involution several homology theories exists, for instance reflexive homology as studied by Graves and involutive Hochschild homology defined by Fernàndez-València and Giansiracusa. We prove that the corresponding homology groups can be identified with the homotopy groups of an equivariant Loday construction of the one-point compactification of the sign-representation evaluated at the trivial orbit, if we assume that $2$ is invertible and if the underlying abelian group of the ring is flat. We also show a relative version where we consider an associative $k$-algebra with an anti-involution where $k$ is an arbitrary ground ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20082 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reflexive homology and involutive Hochschild homology as equivariant Loday constructions Lindenstrauss, Ayelet Richter, Birgit Algebraic Topology For associative rings with anti-involution several homology theories exists, for instance reflexive homology as studied by Graves and involutive Hochschild homology defined by Fernàndez-València and Giansiracusa. We prove that the corresponding homology groups can be identified with the homotopy groups of an equivariant Loday construction of the one-point compactification of the sign-representation evaluated at the trivial orbit, if we assume that $2$ is invertible and if the underlying abelian group of the ring is flat. We also show a relative version where we consider an associative $k$-algebra with an anti-involution where $k$ is an arbitrary ground ring. |
| title | Reflexive homology and involutive Hochschild homology as equivariant Loday constructions |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2407.20082 |