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The spiral index of knots
Published online by Cambridge University Press: 04 June 2010
Abstract
In this paper, we introduce two new invariants that are closely related to Milnor's curvature-torsion invariant. The first, a particularly natural invariant called the spiral index of a knot, captures the number of local maxima in a knot projection that is free of inflection points. This invariant is sandwiched between the bridge and braid index of a knot, and captures more subtle properties. The second invariant, the projective superbridge index, provides a method of counting the greatest number of local maxima that occur in a given projection. In addition to investigating the relationships among these invariants, we use them to classify all those knots for which Milnor's curvature-torsion invariant is 6π.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 149 , Issue 2 , September 2010 , pp. 297 - 315
- Copyright
- Copyright © Cambridge Philosophical Society 2010
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