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arXiv · 2607.01632

Categorification of some Penrose polynomials

D. W. Collison·D. Tubbenhauer
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Abstract

We construct doubly- and triply-graded Penrose-type homologies for ribbon graphs. The construction is a TQFT-valued cube of resolutions built from two-dimensional cobordisms, which may be nonorientable. Their Euler characteristics recover specializations of some Penrose polynomials; in particular, the four color case comes with a refinement of the classical Penrose criterion.

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D. W. Collison, D. Tubbenhauer. 2026-07-02. Categorification of some Penrose polynomials. https://arxiv.org/abs/2607.01632

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