A symmetric monoidal Frohman-Nicas TQFT for sutured manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| _version_ | 1866911447983849472 |
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| author | Manion, Andrew Rutter, Elijah |
| author_facet | Manion, Andrew Rutter, Elijah |
| contents | By analyzing the decategorification of bordered sutured Heegaard Floer homology, we reinterpret and generalize the classical Frohman-Nicas TQFT for the Alexander polynomial in the setting of 3d sutured cobordisms between sutured surfaces. In this setting, the Frohman-Nicas TQFT maps for arbitrary cobordisms between surfaces, with no connectivity restrictions, get interpreted as part of an honest symmetric monoidal functor (under disjoint union) with no half-projectivity zeroes. We also relate the decategorified bordered sutured theory with $\mathrm{Spin}^c$ structures to a sutured version of Florens-Massuyeau's $G$-analogue of the Frohman-Nicas TQFT. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_13552 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A symmetric monoidal Frohman-Nicas TQFT for sutured manifolds Manion, Andrew Rutter, Elijah Geometric Topology Quantum Algebra 57K16 (primary), 57K18, 18N25 (secondary) By analyzing the decategorification of bordered sutured Heegaard Floer homology, we reinterpret and generalize the classical Frohman-Nicas TQFT for the Alexander polynomial in the setting of 3d sutured cobordisms between sutured surfaces. In this setting, the Frohman-Nicas TQFT maps for arbitrary cobordisms between surfaces, with no connectivity restrictions, get interpreted as part of an honest symmetric monoidal functor (under disjoint union) with no half-projectivity zeroes. We also relate the decategorified bordered sutured theory with $\mathrm{Spin}^c$ structures to a sutured version of Florens-Massuyeau's $G$-analogue of the Frohman-Nicas TQFT. |
| title | A symmetric monoidal Frohman-Nicas TQFT for sutured manifolds |
| topic | Geometric Topology Quantum Algebra 57K16 (primary), 57K18, 18N25 (secondary) |
| url | https://arxiv.org/abs/2602.13552 |