Restricted (2+1)-TQFTs supported by thickened and solid tori
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913861567774720 |
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| author | Đorđević, Dušan Kosanović, Danica Nikolić, Jovana Petrić, Zoran |
| author_facet | Đorđević, Dušan Kosanović, Danica Nikolić, Jovana Petrić, Zoran |
| contents | A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21373 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restricted (2+1)-TQFTs supported by thickened and solid tori Đorđević, Dušan Kosanović, Danica Nikolić, Jovana Petrić, Zoran Geometric Topology Category Theory 57K16, 57K30, 57R56, 18A22, 18M05 A faithful $(1+1)$ TQFT has recently been constructed, but the existence of a faithful $(2+1)$ TQFT remains an open question, that subsumes the hard problem of linearity of mapping class groups of surfaces. To circumvent the latter problem we construct a subcategory of the category of 3-cobordisms, containing disjoint unions of tori and simplest cobordisms between them. On this we define TQFTs that are able to distinguish pairs of torus bundles and lens spaces, previously shown not to be distinguishable by quantum invariants. |
| title | Restricted (2+1)-TQFTs supported by thickened and solid tori |
| topic | Geometric Topology Category Theory 57K16, 57K30, 57R56, 18A22, 18M05 |
| url | https://arxiv.org/abs/2505.21373 |