TQFTs do not detect the Milnor sphere
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910003706724352 |
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| author | Gripaios, Ben Randal-Williams, Oscar |
| author_facet | Gripaios, Ben Randal-Williams, Oscar |
| contents | We show that, under very general hypotheses, topological quantum field theories (TQFTs) cannot detect homotopy spheres bounding parallelisable manifolds, such as Milnor's exotic 7-dimensional sphere. The result holds for a wide variety of target categories (or $(\infty,n)$-categories) and arbitrary tangential structures. An appendix contains results on the mapping class groups of (stably-) framed manifolds that may be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20828 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | TQFTs do not detect the Milnor sphere Gripaios, Ben Randal-Williams, Oscar Algebraic Topology High Energy Physics - Theory Mathematical Physics We show that, under very general hypotheses, topological quantum field theories (TQFTs) cannot detect homotopy spheres bounding parallelisable manifolds, such as Milnor's exotic 7-dimensional sphere. The result holds for a wide variety of target categories (or $(\infty,n)$-categories) and arbitrary tangential structures. An appendix contains results on the mapping class groups of (stably-) framed manifolds that may be of independent interest. |
| title | TQFTs do not detect the Milnor sphere |
| topic | Algebraic Topology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2601.20828 |