Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants

Friedl, Stefan¹

¹Department of Mathematics, Rice University, Houston TX 77005, USA

Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 893-934

Résumé

We give a useful classification of the metabelian unitary representations of π1(MK), where MK is the result of zero-surgery along a knot K ⊂ S3. We show that certain eta invariants associated to metabelian representations π1(MK) → U(k) vanish for slice knots and that even more eta invariants vanish for ribbon knots and doubly slice knots. We show that our vanishing results contain the Casson–Gordon sliceness obstruction. In many cases eta invariants can be easily computed for satellite knots. We use this to study the relation between the eta invariant sliceness obstruction, the eta-invariant ribbonness obstruction, and the L2–eta invariant sliceness obstruction recently introduced by Cochran, Orr and Teichner. In particular we give an example of a knot which has zero eta invariant and zero metabelian L2–eta invariant sliceness obstruction but which is not ribbon.

Détail

DOI : 10.2140/agt.2004.4.893

Keywords: knot concordance, Casson–Gordon invariants, Eta invariant

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