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Geometric filtrations of link concordance

#### Robert Schneiderman, CUNY Lehman

Class n gropes are geometric embodiments of length n commutators of group
elements, and it is not known which links in the 3-sphere bound disjointly
embedded class n gropes in the 4-ball. I will describe how counting
intersections among of iterated Whitney disks completely describes the story
for 2-component links through n=6, and modulo connected sums with
boundary links through n=13.
This theory of Whitney towers unifies the known obstructions (Arf, Sato-Levine,
and Milnor invariants) and provides a precise formulation of a new family of
conjectured concordance invariants which are the only possible remaining
obstructions to class n grope null-concordance.