On the functoriality of the space of equivariant smooth $h$-cobordisms

Autor:	Goodwillie, Thomas, Igusa, Kiyoshi, Malkiewich, Cary, Merling, Mona
Rok vydání:	2023
Předmět:	Mathematics - Algebraic Topology Mathematics - Geometric Topology Mathematics - K-Theory and Homology
Druh dokumentu:	Working Paper
Popis:	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. Comment: Small expository changes from the first version. 65 pages. Comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2303.14892 Zobrazit plný text záznamu View this record from Arxiv