Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.
Generalized duality for graphs on surfaces and the signed Bollobas-Riordan polynomial
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abstract
We generalize the natural duality of graphs embedded into a surface to a duality with respect to a subset of edges. The dual graph might be embedded into a different surface. We prove a relation between the signed Bollobas-Riordan polynomials of dual graphs. This relation unifies various recent results expressing the Jones polynomial of links as specializations of the Bollobas-Riordan polynomials.
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math.CO 1years
2026 1verdicts
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Categorification of some Penrose polynomials
Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.