Topological CoHochschild Homology and Thom Spectra
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915735347920896 |
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| author | Zha, Jiaxi |
| author_facet | Zha, Jiaxi |
| contents | For an $\E$-ring spectrum $R$ and a map $f:X\to Pic(R)$ of spaces, the Thom spectrum $\T f$ is a comodule over $R\otimes\Si X$. In this parper we study the topological coHochschild homology of $R\otimes\Si X$ with coefficient $\T f$. More concretely, for a simply connected space $X$, we will give a filtration on $\mathrm{coTHH}^R(\T f;R\otimes\Si X)$ via the cellular structure of $X$. Furthermore, we will reduce the computation of $\mathrm{coTHH}^R(\T f;R\otimes\Si X)$ to that of $\mathrm{coTHH}^R(R\otimes\Si G)$ for some group-like $\mathbb{E}_1$-spaces. Finally, we will use these results to study properties of $\mathrm{coTHH}(\T f;R\otimes\Si X)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11263 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological CoHochschild Homology and Thom Spectra Zha, Jiaxi Algebraic Topology For an $\E$-ring spectrum $R$ and a map $f:X\to Pic(R)$ of spaces, the Thom spectrum $\T f$ is a comodule over $R\otimes\Si X$. In this parper we study the topological coHochschild homology of $R\otimes\Si X$ with coefficient $\T f$. More concretely, for a simply connected space $X$, we will give a filtration on $\mathrm{coTHH}^R(\T f;R\otimes\Si X)$ via the cellular structure of $X$. Furthermore, we will reduce the computation of $\mathrm{coTHH}^R(\T f;R\otimes\Si X)$ to that of $\mathrm{coTHH}^R(R\otimes\Si G)$ for some group-like $\mathbb{E}_1$-spaces. Finally, we will use these results to study properties of $\mathrm{coTHH}(\T f;R\otimes\Si X)$. |
| title | Topological CoHochschild Homology and Thom Spectra |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2601.11263 |