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      Slopes and signatures of links

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      Author(s)
      Degtyarev, Alex
      Florens, V.
      Lecuona, A.G.
      Date
      2022-03-14
      Source Title
      Fundamenta Mathematicae
      Electronic ISSN
      1730-6329
      Publisher
      Instytut Matematyczny,Polish Academy of Sciences, Institute of Mathematics
      Volume
      258
      Issue
      2022
      Pages
      65 - 114
      Language
      English
      Type
      Article
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      Abstract
      We define the slope of a colored link in an integral homology sphere, associated to admissible characters on the link group. Away from a certain singular locus, the slope is a rational function which can be regarded as a multivariate generalization of the Kojima–Yamasaki η-function. It is the ratio of two Conway potentials, provided that the latter makes sense; otherwise, it is a new invariant. The slope is responsible for an extra correction term in the signature formula for the splice of two links, in the previously open exceptional case where both characters are admissible. Using a similar construction for a special class of tangles, we formulate generalized skein relations for the signature.
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      http://hdl.handle.net/11693/111948
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