{"paper":{"title":"$L^2$--eta--invariants and their approximation by unitary eta--invariants","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Stefan Friedl","submitted_at":"2003-05-28T15:20:18Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0305401","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}