A Casson–Lin type invariant for links

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In searching for methods to distinguish knots and links, recent work has focussed on the more general virtual knots and links, introduced by Kauffman in [2]. If we ignore the over/under information at each crossing, we obtain a flat virtual knot or link (still called a knot or a link), sometimes called the universe of the original virtual knot or link. It is a triviality that if the original vi...

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One of the characteristic features of the fundamental group of a closed 3manifold is that its representation variety in a compact Lie group tends to be finite, in a properly understood sense. This has been a guiding principle for defining invariants of 3-manifolds ever since Casson defined his λ-invariant for integral homology 3-spheres via a signed count of the SU(2) representations of the fun...

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We construct an invariant of boundary links which is at least as strong as the Kontsevich integral, determines the S-equivalence class of a boundary link and which takes values in a space of trivalent graphs whose edges are decorated by rational functions in noncommuting variables. Our invariant is axiomatically characterized by a universal property closely related to the Homology Surgery view ...

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ژورنال

عنوان ژورنال: Pacific Journal of Mathematics

سال: 2010

ISSN: 0030-8730,0030-8730

DOI: 10.2140/pjm.2010.248.139