$L^2$--eta--invariants and their approximation by unitary eta--invariants

Details $L^2$--eta--invariants and their approximation by unitary eta--invariants $L^2$--eta--invariants and their approximation by unitary eta--invariants

2003-05-28

arxiv.org/abs/math/0305401v1

Mathematics

Geometric Topology

13 pages

Scientific paper

Cochran, Orr and Teichner introduced $L^2$--eta--invariants to detect highly non--trivial examples of non slice knots. Using a recent theorem by L\"uck and Schick we show that their metabelian $L^2$--eta--invariants can be viewed as the limit of finite dimensional unitary representations. We recall a ribbon obstruction theorem proved by the author using finite dimensional unitary eta--invariants. We show that if for a knot $K$ this ribbon obstruction vanishes then the metabelian $L^2$--eta--invariant vanishes too. The converse has been shown by the author not to be true.

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