JSJ decompositions of knot exteriors, Dehn surgery and the L-space conjecture

• Steven Boyer ^[1] ; Cameron McA. Gordon ^[2] ; Ying Hu ^[3]
  1. [1] University of Quebec at Montreal

     University of Quebec at Montreal

     Canadá

     
  2. [2] University of Texas at Austin

     University of Texas at Austin

     Estados Unidos

     
  3. [3] University of Nebraska System

     University of Nebraska System

     Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 1, 2025
• Idioma: inglés
• Enlaces
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• Resumen

  • In this article, we apply slope detection techniques to study properties of toroidal 3- manifolds obtained by performing Dehn surgeries on satellite knots in the context of the L-space conjecture. We show that if K is an L-space knot or admits an irreducible rational surgery with non-left-orderable fundamental group, then the JSJ graph of its exterior is a rooted interval. Consequently, any rational surgery on a composite knot has a left-orderable fundamental group. This is the left-orderable counterpart of Krcatovich’s result on the primeness of L-space knots, which we reprove using our methods. Analogous results on the existence of co-orientable taut foliations are proved when the knot has a fibred companion. Our results suggest a new approach to establishing the counterpart of Krcatovich’s result for surgeries with co-orientable taut foliations, on which partial results have been achieved by Delman and Roberts.

    Finally, we prove results on left-orderable p/q-surgeries on knots with p small.

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