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arXiv · 2602.13552

A symmetric monoidal Frohman-Nicas TQFT for sutured manifolds

Andrew Manion·Elijah Rutter
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Abstract

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.

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Andrew Manion, Elijah Rutter. 2026-02-14. A symmetric monoidal Frohman-Nicas TQFT for sutured manifolds. https://arxiv.org/abs/2602.13552

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