Exact Triangles for SO(3) Instanton Homology of Webs
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1508.07207.pdf
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336.47 KB
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91b1fa75e354dcbe06b4426862c37079
Author(s)
Kronheimer, P. B.
Mrowka, Tomasz S
Date Issued
May 2016
Journal
Journal of Topology
Publisher
Oxford University Press (OUP)
Citation
Kronheimer, P. B., and T. S. Mrowka. “Exact Triangles for SO(3) Instanton Homology of Webs.” Journal of Topology 9, 3 (May 2016): 774–796 © 2016 London Mathematical Society
Version
Original manuscript
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1112/JTOPOL/JTW010
