Topology & Geometric Group Theory Seminar

Spring 2009

1:30 – 2:30, Malott 207

Thursday, March 12

Jim Conant, University of Tennessee

Quasi Lie algebras and concordance invariants of links

The question of whether a link bounds a union of (flat) disks into the 4-ball is an extremely subtle one. Rather than answer this question in full, we ask when can a simpler situation happen, namely can a link bound a "Whitney Tower" into the 4-ball. A Whitney tower is a type of 2-complex which approximates a disk better and better as the order of the tower increases. We propose a complete obstruction theory for Whitney towers, which is to say if a set of invariants vanishes, then one can extend the tower to a tower of one higher order. There are currently two "obstructions" to completing this program. The first obstruction is an algebraic problem concerning whether torsion exists in a certain abelian group of labeled trees. (The so-called Levine conjecture.) The second obstruction is that although we can compute almost all the invariants of Whitney towers in terms of Milnor invariants, there is still a hierarchy of unknown 2-torsion invariants which is needed to complete the theory. This work is Joint with Rob Schneiderman and Peter Teichner

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