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Abstract: We define a set of -second-order- L^2-signature invariants for anyalgebraically slice knot. These obstruct a knot-s being a slice knot andgeneralize Casson-Gordon invariants, which we consider to be -first-ordersignatures-. As one application we prove: If K is a genus one slice knot then,on any genus one Seifert surface, there exists a homologically essential simpleclosed curve of self-linking zero, which has vanishing zero-th order signatureand a vanishing first-order signature. This extends theorems of Cooper andGilmer. We introduce a geometric notion, that of a derivative of a knot withrespect to a metabolizer. We also introduce a new equivalence relation,generalizing homology cobordism, called null-bordism.



Autor: Tim Cochran, Shelly Harvey, Constance Leidy

Fuente: https://arxiv.org/







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