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Universal construction of topological theories in two dimensions

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arxiv 2007.03361 v1 pith:ZISJSVGD submitted 2020-07-07 math.QA math.GTmath.RT

Mikhail Khovanov This is my paper · ORCID
classification math.QAmath.GTmath.RT
keywords theoriesschurconstructionextensionformulafunctionspolynomialsrational
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We consider Blanchet, Habegger, Masbaum and Vogel's universal construction of topological theories in dimension two, using it to produce interesting theories that do not satisfy the usual two-dimensional TQFT axioms. Kronecker's characterization of rational functions allows us to classify theories over a field with finite-dimensional state spaces and introduce their extension to theories with the ground ring the product of rings of symmetric functions in N and M variables. We look at several examples of non-multiplicative theories and see Hankel matrices, Schur and supersymmetric Schur polynomials quickly emerge from these structures. The last section explains how an extension of the Robert-Wagner foam evaluation to overlapping foams gives the Sergeev-Pragacz formula for the supersymmetric Schur polynomials and the Day formula for the Toeplitz determinant of rational power series as special cases.

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Cited by 3 Pith papers

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

  1. From Multipartite Entanglement to TQFT

    hep-th 2026-02 conditional novelty 7.0 of 10

    Genuine multipartite entanglement of a gapped ground state is conjectured and, for Levin-Wen models, shown to reproduce the TQFT partition function on any 3-manifold.

  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.

  3. Lectures on SL(3) foams and link homology

    math.QA 2025-07 conditional novelty 1.0 of 10

    This is an expository review of SL(3) foam evaluation and its use in categorifying the Kuperberg quantum invariant, with no new theorems.

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