Geometric filtrations of string links and homology cylinders

(Joint with Schneiderman and Teichner)
We analyze several filtrations on the groups of concordance classes of string links and homology
cylinders modulo homology bordism. In particular we compare the twisted Whitney tower
filtration of string links to the Johnson filtration of string links, showing that the associated
graded groups differ by finitely generated 2-torsion groups, corresponding to higher-order
Arf invariants. We also continue Jerry Levine's analysis of the Johnson filtration of homology
cylinders to the filtration defined by embedded surgery along claspers, completely characterizing
the difference up to some unknown 2-torsion.

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