Grope cobordism of classical knots
by
James Conant
Cornell University

I present an infinite class of equivalence relations on knots, indexed by rooted trivalent trees (or more generally rooted unitrivalent graphs), defined by a certain refinement of ambient cobordism. These equivalence relations contain Vassiliev n-equivalence, as well as relations that are not of finite type. For instance I will show that S-equivalence is encompassed. Hwoever, most of these equivalence relations have not been fully analyzed and the most we can say is that they preserve things like concordance class, S-equivalence class , type k Vassiliev invariants etc, depending on certain properties of the unitrivalent graph.

Date received: March 20, 2001