Stably diffeomorphic manifolds and the realisation of modified surgery obstructions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866916331986616320 |
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| author | Conway, Anthony Crowley, Diarmuid Powell, Mark Sixt, Joerg |
| author_facet | Conway, Anthony Crowley, Diarmuid Powell, Mark Sixt, Joerg |
| contents | For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In fact we construct infinitely many such infinite sets. To achieve this we prove a realisation result for appropriate subsets of Kreck's modified surgery monoid $\ell_{2q+1}(\mathbb{Z}[π])$, analogous to Wall's realisation of the odd-dimensional surgery obstruction $L$-group $L_{2q+1}^s(\mathbb{Z}[π])$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05632 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Stably diffeomorphic manifolds and the realisation of modified surgery obstructions Conway, Anthony Crowley, Diarmuid Powell, Mark Sixt, Joerg Geometric Topology 57R65, 56R67 For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In fact we construct infinitely many such infinite sets. To achieve this we prove a realisation result for appropriate subsets of Kreck's modified surgery monoid $\ell_{2q+1}(\mathbb{Z}[π])$, analogous to Wall's realisation of the odd-dimensional surgery obstruction $L$-group $L_{2q+1}^s(\mathbb{Z}[π])$. |
| title | Stably diffeomorphic manifolds and the realisation of modified surgery obstructions |
| topic | Geometric Topology 57R65, 56R67 |
| url | https://arxiv.org/abs/2109.05632 |