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2004 Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants
Stefan Friedl
Algebr. Geom. Topol. 4(2): 893-934 (2004). DOI: 10.2140/agt.2004.4.893


We give a useful classification of the metabelian unitary representations of π1(MK), where MK is the result of zero-surgery along a knot KS3. 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.


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Stefan Friedl. "Eta invariants as sliceness obstructions and their relation to Casson–Gordon invariants." Algebr. Geom. Topol. 4 (2) 893 - 934, 2004.


Received: 17 January 2004; Revised: 13 September 2004; Accepted: 19 September 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1067.57003
MathSciNet: MR2100685
Digital Object Identifier: 10.2140/agt.2004.4.893

Primary: 57M25, 57M27, 57Q45, 57Q60

Rights: Copyright © 2004 Mathematical Sciences Publishers


Vol.4 • No. 2 • 2004
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