Exact triangles for SO(3) instanton homology of webs

Abstract

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.

References in corpus (1)

• Tait colorings, and an instanton homology for webs and foams

Cited by in corpus (6)

• A deformation of instanton homology for webs
• Two-fold quasi-alternating links, Khovanov homology and instanton homology
• Tait colorings, and an instanton homology for webs and foams
• Anchored foams and annular homology
• A Cohomology Theory for Planar Trivalent Graphs with Perfect Matchings
• sl(3) Khovanov module and the detection of the planar theta-graph