Tree homology and a conjecture of Levine

In a joint project with Rob Schneiderman and Peter Teichner, we have analyzed the structure of the set of links up to "Whitney tower concordance." A crucial aspect of this analysis is a conjecture of Jerry Levine, which relates an algebraically defined Lie ring to a combinatorially defined abelian group of labeled trees modulo the IHX relation. This conjecture is easy to verify after tensoring with a field of characteristic $0$, but the general statement is not so easy. In this talk, I will discuss the conjecture and how we proved it using discrete Morse theory for chain complexes.

http://people.mpim-bonn.mpg.de/teichner/Math/4-Manifolds.html