Constructs doubly- and triply-graded Penrose-type homologies for ribbon graphs via TQFT cube of resolutions whose Euler characteristics recover Penrose polynomial specializations.
Tait colorings, and an instanton homology for webs and foams
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abstract
We use SO(3) gauge theory to define a functor from a category of unoriented webs and foams to the category of finite-dimensional vector spaces over the field of two elements. We prove a non-vanishing theorem for this SO(3) instanton homology of webs, using Gabai's sutured manifold theory. It is hoped that the non-vanishing theorem may support a program to provide a new proof of the four-color theorem.
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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.