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Legendrian and transverse cables of positive torus knots

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  • John Etnyre, Georgia Institute of Technology, United States
  • Douglas LaFountain, Denmark
  • Bülent Tosun, Georgia Institute of Technology, United States
In this paper we classify Legendrian and transverse knots in the knot types obtained from positive torus knots by cabling. This classification allows us to demonstrate several new phenomena. Specifically, we show there are knot types that have non-destabilizable Legendrian representatives whose Thurston-Bennequin invariant is arbitrarily far from maximal. We also exhibit Legendrian knots requiring arbitrarily many stabilizations before they become Legendrian isotopic. Similar new phenomena are observed for transverse knots. To achieve these results we define and study "partially thickenable" tori, which allow us to completely classify solid tori representing positive torus knots.
Original languageEnglish
JournalGeometry & Topology
Pages (from-to)1639-1689
Number of pages51
Publication statusPublished - 2012

    Research areas

  • Legendrian, contact, cable, torus knot

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