On automorphisms of high-dimensional solid tori
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866910538181640192 |
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| author | Bustamante, Mauricio Randal-Williams, Oscar |
| author_facet | Bustamante, Mauricio Randal-Williams, Oscar |
| contents | We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \times D^{2n-1}$, for $2n \geq 6$, in a range of degrees up to $n-2$. Our analysis relies on understanding the homotopy fibre of a linearisation map from the plus-construction of the classifying space of certain space of self-embeddings of stabilisations of this manifold to a form of Hermitian $K$-theory of the integral group ring of $π_1(S^1)$. We also show that these homotopy groups vanish rationally. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_10887 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On automorphisms of high-dimensional solid tori Bustamante, Mauricio Randal-Williams, Oscar Algebraic Topology Geometric Topology 55R40, 58D10, 57S05 We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \times D^{2n-1}$, for $2n \geq 6$, in a range of degrees up to $n-2$. Our analysis relies on understanding the homotopy fibre of a linearisation map from the plus-construction of the classifying space of certain space of self-embeddings of stabilisations of this manifold to a form of Hermitian $K$-theory of the integral group ring of $π_1(S^1)$. We also show that these homotopy groups vanish rationally. |
| title | On automorphisms of high-dimensional solid tori |
| topic | Algebraic Topology Geometric Topology 55R40, 58D10, 57S05 |
| url | https://arxiv.org/abs/2010.10887 |