{
  "id": "math/0305402",
  "version": "v3",
  "published": "2003-05-28T15:33:38.000Z",
  "updated": "2004-10-27T20:35:46.000Z",
  "title": "Eta invariants as sliceness obstructions and their relation to Casson-Gordon invariants",
  "authors": [
    "Stefan Friedl"
  ],
  "comment": "Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-39.abs.html",
  "journal": "Algebr. Geom. Topol. 4 (2004) 893-934",
  "categories": [
    "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2004-10-27T20:35:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "57M27",
      "57Q45",
      "57Q60"
    ],
    "keywords": [
      "casson-gordon invariants",
      "slice knots",
      "eta invariant sliceness obstruction",
      "casson-gordon sliceness obstruction",
      "zero eta invariant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}