An infinity-categorical TQFT from instantons

@misc{ye2026infinitycategorical,
  title = {{An infinity-categorical TQFT from instantons}},
  author = {Fan Ye},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.29902},
  eprint = {2606.29902},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.29902},
}

TY  - UNPB
TI  - An infinity-categorical TQFT from instantons
AU  - Fan Ye
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2606.29902
UR  - https://arxiv.org/abs/2606.29902
AB  - In this paper, we lift the instanton TQFT from ordinary categories to the ∞-categorical setting by constructing a functor CI:BI^∂⟶D from an ∞-cobordism category BI^∂ for instantons to an ∞-derived category D of $2$-periodic chain complexes. The construction of BI^∂ is a modification of the ∞-cobordism category Bord_4 introduced by Lurie and by Calaque--Scheimbauer using complete Segal spaces. The target ∞-category D is obtained via the dg nerve of the dg category of $2$-periodic chain complexes of finitely presented projective ℤ-modules. The information encoded by the functor CI was already developed by Kronheimer--Mrowka using families of metrics on cobordisms. Our reinterpretation in terms of ∞-categories conceptually simplifies the construction of the hypercube complexes underlying the link spectral sequence. This viewpoint also clarifies hyperbox complexes and compression in Manolescu--Ozsváth's work, and possible A_∞-structures, especially their signs and higher coherence. In addition, we lift the generalized cap product μ-operators in instanton Floer homology to the chain level and construct explicit homotopies and higher homotopies establishing the commutativity of multiple μ-operators in even degrees.
ER  -