Elliptic Curves and Knot Homology

Elliptic Curves and Knot Homology

-
Lucas Culler, MIT
Fine Hall 314

Given a smooth elliptic curve E over the complex numbers we construct a functor-valued invariant of tangles, extending a known braid group action on the derived category of coherent sheaves on E^n.  The invariant associated to a closed link L is related to odd Khovanov homology, and can be described in terms of the double cover branched over L.