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From finite state automata to tangle cobordisms: a TQFT journey from one to four dimensions

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arxiv 2309.00708 v2 pith:BJSE3M4Z submitted 2023-09-01 math.QA cs.FLmath-phmath.CTmath.MPmath.RT

Mee Seong Im , Mikhail Khovanov This is my paper · ORCID
classification math.QAcs.FLmath-phmath.CTmath.MPmath.RT
keywords automatafinitelinkstatebooleanbriefcategorifycobordisms
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abstract

This is a brief introduction to link homology theories that categorify Reshetikhin--Turaev $\mathsf{SL}(N)$-quantum link invariants. A recently discovered surprising connection between finite state automata and Boolean TQFTs in dimension one is explained as a warm-up.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Formal Languages and TQFTs with Defects

    math-ph 2024-12 conditional novelty 6.0 of 10

    A Boolean 1D TQFT-with-defects construction for regular languages is shown to be functorial under transducers and generalized to context-free grammars via an operadic Chomsky-Schützenberger theorem.

  2. Diagrammatics of information

    math-ph 2025-02 conditional novelty 3.0 of 10

    Shannon and joint entropy are recast as sums of infinitesimal dilogarithm brackets, and the five-term dilogarithm is deformed to the four-term infinitesimal dilogarithm via dual numbers.

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