Stefan Friedl Research Statement

Recent Research: Slice knots. A knot K ⊂ S is called slice, if it bounds a smooth 2-disk in D. In higher odd dimensions Levine [Le69], [Le69b] found a computable algebraic method of determining whether a knot is slice or not. In 1975 Casson and Gordon [CG86] first found examples which show that the high dimensional results (which relied on the Whitney trick) can not be extended to the case of one dimensional knots. Recently Cochran, Orr and Teichner [COT03] constructed an infinite series of obstructions to finding slice disks for a given knot and used L–eta invariants to detect highly non–trivial examples. In my thesis [Fr04] I used (finite dimensional) eta invariants, introduced by Atiyah, Patodi and Singer [APS75], to give obstructions to a knot being slice. I also show that these obstructions contain and slightly extend the obstructions of Casson and Gordon (cf. also [Fr05e]). It follows from work of Taehee Kim [Ki04] and myself [Fr04] that the eta invariant obstruction is independent of the L–eta invariant obstruction, i.e. there are knots which have non-zero eta invariants but zero L–eta invariants and vice versa.