Witten’s approach to Khovanov homology of knots is based on the five-dimensional system of partial differential equations, which we call Haydys–Witten equations. We argue for a one-to-one correspondence between its solutions and solutions of the seven-dimensional system of equations. The latter can be formulated on any G2 holonomy manifold and is a close cousin of the monopole equation of Bogomolny. Octonions play the central role in our view, in which both the seven-dimensional equations and the Haydys–Witten equations appear as reductions of the eight-dimensional Spin(7) instanton equation.
- Gauge theory
- special holonomy
ASJC Scopus subject areas
- Mathematical Physics
- Statistical and Nonlinear Physics