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Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants | | Stefan Friedl
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28 May 2003 | | Journal: | Algebr. Geom. Topol. 4 (2004) 893-934 | | Subject: | Geometric Topology MSC-class: 57M25, 57M27; 57Q45, 57Q60 | math.GT | | Abstract: | We give a useful classification of the metabelian unitary representations of pi_1(M_K), where M_K is the result of zero-surgery along a knot K in S^3. We show that certain eta invariants associated to metabelian representations pi_1(M_K) --> 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 L^2-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 L^2-eta invariant sliceness obstruction but which is not ribbon. | | Source: | arXiv, math.GT/0305402 | | Services: | Forum | Review | PDF | Favorites | |
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