Derivatives of Knots and Second-order Signatures - Mathematics > Geometric TopologyReport as inadecuate




Derivatives of Knots and Second-order Signatures - Mathematics > Geometric Topology - Download this document for free, or read online. Document in PDF available to download.

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.



Author: Tim Cochran, Shelly Harvey, Constance Leidy

Source: https://arxiv.org/







Related documents