Octonions, Monopoles, and Knots

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11 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)641-659
Number of pages19
JournalLetters in Mathematical Physics
Issue number5
StatePublished - May 1 2015


  • Gauge theory
  • knots
  • octonions
  • special holonomy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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