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Finite type invariants of
knots in homology $3$–spheres with respect to null
LP–surgeries
Delphine Moussard |
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Geometry & Topology 23 (2019) 2005–2050
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Abstract |
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We study a theory of finite type invariants for nullhomologous knots in rational homology –spheres with respect to null Lagrangian-preserving surgeries. It is an analogue in the setting of the rational homology of the Garoufalidis–Rozansky theory for knots in integral homology –spheres. We give a partial combinatorial description of the graded space associated with our theory and determine some cases when this description is complete. For nullhomologous knots in rational homology –spheres with a trivial Alexander polynomial, we show that the Kricker lift of the Kontsevich integral and the Lescop equivariant invariant built from integrals in configuration spaces are universal finite type invariants for this theory; in particular, this implies that they are equivalent for such knots. |
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Keywords
3-manifold, knot, homology sphere, beaded Jacobi diagram,
Kontsevich integral, Borromean surgery, null-move,
Lagrangian-preserving surgery, finite type invariant
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Mathematical Subject Classification 2010
Primary: 57M27
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References |
Publication
Received: 5 November 2017
Revised: 13 September 2018
Accepted: 15 November 2018
Published: 17 June 2019
Proposed: Cameron Gordon
Seconded: András I Stipsicz, Walter Neumann
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Authors |
| Delphine Moussard | |
| Institut de Mathématiques de
Bourgogne Université de Bourgogne Dijon France |
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