This is the first of a two part series on work with Peter Kronheimer. In this talk I will describe a variant of Instanton Floer homology for knots or more generally webs (embedded trivalent graphs) in 3-manifolds. The interesting twist in the story is introducing a local coefficient group which seems to require the use of webs (rather than knots). For certain specializations of this local system the resulting homology groups admit a spectral sequence whose $E_2$-term is Bar-Natan’s variant of Khovanov homology providing a geometric interpretation of that theory.  I’ll try to sketch some of this story.

Kronheimer’s talk the following week will describe further (potential) applications of these groups.