Real Hochschild homology as an equivariant Loday construction
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911512164040704 |
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| author | Lindenstrauss, Ayelet Richter, Birgit Zou, Foling |
| author_facet | Lindenstrauss, Ayelet Richter, Birgit Zou, Foling |
| contents | Equivariant Loday constructions are a means for providing geometric interpretations of equivariant homology theories. They are usually constructed for a simplicial $G$-set and a $G$-Tambara functor. We study situations where -- depending on the isotropy subgroups occurring in the simplicial $G$-set -- one can work with $H$-Tambara functors for a suitable subgroup $H$ of $G$. We apply this to give an interpretation of Real Hochschild homology of discrete $E_σ$-rings as equivariant Loday constructions where we consider $2m$-gons with a geometrically defined action of the dihedral groups $D_{2m}$ for all $m \geq 1$. The action of symmetric groups on $1$-skeleta of permutohedra also gives examples with isotropy groups $C_2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12803 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Real Hochschild homology as an equivariant Loday construction Lindenstrauss, Ayelet Richter, Birgit Zou, Foling Algebraic Topology Equivariant Loday constructions are a means for providing geometric interpretations of equivariant homology theories. They are usually constructed for a simplicial $G$-set and a $G$-Tambara functor. We study situations where -- depending on the isotropy subgroups occurring in the simplicial $G$-set -- one can work with $H$-Tambara functors for a suitable subgroup $H$ of $G$. We apply this to give an interpretation of Real Hochschild homology of discrete $E_σ$-rings as equivariant Loday constructions where we consider $2m$-gons with a geometrically defined action of the dihedral groups $D_{2m}$ for all $m \geq 1$. The action of symmetric groups on $1$-skeleta of permutohedra also gives examples with isotropy groups $C_2$. |
| title | Real Hochschild homology as an equivariant Loday construction |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2603.12803 |