On the functoriality of the space of equivariant smooth $h$-cobordisms
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917993177415680 |
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| author | Goodwillie, Thomas Igusa, Kiyoshi Malkiewich, Cary Merling, Mona |
| author_facet | Goodwillie, Thomas Igusa, Kiyoshi Malkiewich, Cary Merling, Mona |
| contents | We construct an $(\infty,1)$-functor that takes each smooth $G$-manifold with corners $M$ to the space of equivariant smooth $h$-cobordisms ${\mathcal H}_{\mathrm{Diff}}(M)$. We also give a stable analogue ${\mathcal H}^{\mathcal U}_{\mathrm{Diff}}(M)$ where the manifolds are stabilized with respect to representation discs. The functor structure is subtle to construct, and relies on several new ideas. In the non-equivariant case $G=e$, our $(\infty,1)$-functor agrees with previous constructions of the smooth $h$-cobordism space as a functor to the homotopy category. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_14892 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the functoriality of the space of equivariant smooth $h$-cobordisms Goodwillie, Thomas Igusa, Kiyoshi Malkiewich, Cary Merling, Mona Algebraic Topology Geometric Topology K-Theory and Homology We construct an $(\infty,1)$-functor that takes each smooth $G$-manifold with corners $M$ to the space of equivariant smooth $h$-cobordisms ${\mathcal H}_{\mathrm{Diff}}(M)$. We also give a stable analogue ${\mathcal H}^{\mathcal U}_{\mathrm{Diff}}(M)$ where the manifolds are stabilized with respect to representation discs. The functor structure is subtle to construct, and relies on several new ideas. In the non-equivariant case $G=e$, our $(\infty,1)$-functor agrees with previous constructions of the smooth $h$-cobordism space as a functor to the homotopy category. |
| title | On the functoriality of the space of equivariant smooth $h$-cobordisms |
| topic | Algebraic Topology Geometric Topology K-Theory and Homology |
| url | https://arxiv.org/abs/2303.14892 |