Diffeomorphism groups of solid tori and the rational pseudoisotopy stable range
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arXiv
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| Natura: | Preprint |
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2026
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| author | Fernandes, João Lobo Muñoz-Echániz, Samuel |
| author_facet | Fernandes, João Lobo Muñoz-Echániz, Samuel |
| contents | We compute the rational homotopy groups of the classifying space $\mathrm{BDiff}_{\partial}(S^1 \times D^{d-1})$ of the topological group of diffeomorphisms of $S^1 \times D^{d-1}$ fixing the boundary for $d \geq 6$, in a range of degrees up until around $d$. This extends results of Budney-Gabai, Bustamante-Randal-Williams, and Watanabe.
As consequences of this computation, we determine the rational pseudoisotopy stable range for compact spin manifolds with fundamental group $\mathbf{Z}$ of dimension $d\geq 6$ to be $[0,d-5]$, and compute in this range the rational homotopy groups of $\mathrm{BDiff}_{\partial}(S^1 \times N)$ for compact simply-connected spin $(d-1)$-manifolds $N$. Finally, by combining our results with work of Krannich-Randal-Williams and Kupers-Randal-Williams on $\mathrm{BDiff}_{\partial}(D^d)$, we compute the rational homotopy groups of the space $\mathrm{Emb}_{\partial}(D^{d-2}, D^d)$ of long knots in codimension 2 for $d \geq 6$, again in the same range. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Diffeomorphism groups of solid tori and the rational pseudoisotopy stable range Fernandes, João Lobo Muñoz-Echániz, Samuel Algebraic Topology Geometric Topology 57S05, 58D10, 55R40, 19D55 We compute the rational homotopy groups of the classifying space $\mathrm{BDiff}_{\partial}(S^1 \times D^{d-1})$ of the topological group of diffeomorphisms of $S^1 \times D^{d-1}$ fixing the boundary for $d \geq 6$, in a range of degrees up until around $d$. This extends results of Budney-Gabai, Bustamante-Randal-Williams, and Watanabe. As consequences of this computation, we determine the rational pseudoisotopy stable range for compact spin manifolds with fundamental group $\mathbf{Z}$ of dimension $d\geq 6$ to be $[0,d-5]$, and compute in this range the rational homotopy groups of $\mathrm{BDiff}_{\partial}(S^1 \times N)$ for compact simply-connected spin $(d-1)$-manifolds $N$. Finally, by combining our results with work of Krannich-Randal-Williams and Kupers-Randal-Williams on $\mathrm{BDiff}_{\partial}(D^d)$, we compute the rational homotopy groups of the space $\mathrm{Emb}_{\partial}(D^{d-2}, D^d)$ of long knots in codimension 2 for $d \geq 6$, again in the same range. |
| title | Diffeomorphism groups of solid tori and the rational pseudoisotopy stable range |
| topic | Algebraic Topology Geometric Topology 57S05, 58D10, 55R40, 19D55 |
| url | https://arxiv.org/abs/2602.08140 |