Derivatives of knots and second-order signatures

@inproceedings{Harvey2008DerivativesOK,
  title={Derivatives of knots and second-order signatures},
  author={Shelly L. Harvey},
  year={2008}
}
We define a set of “second-order” L-signature invariants for any algebraically slice knot. These obstruct a knot’s being a slice knot and generalize Casson-Gordon invariants, which we consider to be “first-order signatures”. As one application we prove: If K is a genus one slice knot then, on any genus one Seifert surface Σ, there exists a homologically essential simple closed curve J of self-linking zero, which has vanishing zero-th order signature and a vanishing first-order signature. This… CONTINUE READING

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