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Exact triangles for SO(3) instanton homology of webs

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arxiv 1508.07207 v1 pith:FEFXLZLC submitted 2015-08-28 math.GT math.CO

P. B. Kronheimer , T. S. Mrowka This is my paper · ORCID
classification math.GTmath.CO
keywords homologyinstantonauthorsexactoctahedralwebsassociatesaxiom
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The SO(3) instanton homology recently introduced by the authors associates a finite-dimensional vector space over the field of two elements to every embedded trivalent graph (or "web"). The present paper establishes a skein exact triangle for this instanton homology, as well as a realization of the octahedral axiom. From the octahedral diagram, one can derive equivalent reformulations of the authors' conjecture that, for planar webs, the rank of the instanton homology is equal to the number of Tait colorings.

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  1. Computer Bounds for Kronheimer-Mrowka Foam Evaluation

    math.GT 2019-08 conditional novelty 6.0 of 10

    For two nonreducible planar graphs the computed dimension of a Khovanov-Robert foam invariant exactly matches the Tait number; for the dodecahedral graph the computation leaves dimensions 58 or 60, with evidence point...

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