Exact triangles for SO(3) instanton homology of webs. (23rd May 2016)

• Record Type: Journal Article
• Authors: Kronheimer, P. B.; Mrowka, T. S.
• Is Part Of: Journal of topology. Volume 9:Part 3(2016)
• Page Start: 774
• Page End: 796
• Publication Date: 2016-05-23
• Subjects: Topology -- Periodicals; 514.05
• DOI: 10.1112/jtopol/jtw010
• Languages: English
• ISSNs: 1753-8416

Abstract

Abstract : The $\mathit {SO}(3)$ 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.