Geometry & Topology

Finite type invariants of knots in homology $3$–spheres with respect to null LP–surgeries

Delphine Moussard

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Abstract

We study a theory of finite type invariants for nullhomologous knots in rational homology 3–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 3–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 3–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.

Article information

Source
Geom. Topol., Volume 23, Number 4 (2019), 2005-2050.

Dates
Received: 5 November 2017
Revised: 13 September 2018
Accepted: 15 November 2018
First available in Project Euclid: 16 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.gt/1563242524

Digital Object Identifier
doi:10.2140/gt.2019.23.2005

Mathematical Reviews number (MathSciNet)
MR3988091

Zentralblatt MATH identifier
07094912

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds

Keywords
3-manifold knot homology sphere beaded Jacobi diagram Kontsevich integral Borromean surgery null-move Lagrangian-preserving surgery finite type invariant

Citation

Moussard, Delphine. Finite type invariants of knots in homology $3$–spheres with respect to null LP–surgeries. Geom. Topol. 23 (2019), no. 4, 2005--2050. doi:10.2140/gt.2019.23.2005. https://projecteuclid.org/euclid.gt/1563242524


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