Equivariance and finite type invariants in dimension 3
type: Dataset
description: This thesis contains a study of finite type invariants of rational homology 3-spheres, and of null-homologous knots in these spheres. The main results are described in Chapter 2, and proved in Chapters 3 to 6. Chapter 3 is an article entitled ``Finite type invariants of rational homology 3-spheres'', to appear in Algebraic & Geometric Topology. In this article, we describe the graded space associated with the filtration of the rational vector space generated by rational homology spheres, defined by rational Lagrangian-preserving surgeries. Chapter 4 is an article entitled ``On Alexander modules and Blanchfield forms of null-homologous knots in rational homology spheres'', published in Journal of Knot Theory and its Ramifications. It contains the classification of the Alexander modules of null-homologous knots in rational homology spheres, and a study of the Blanchfield forms defined on these modules. In the sequel, we consider pairs (M,K) made of a rational homology sphere M and a null-homologous knot K in M. In Chapter 5, we prove that two such pairs have isomorphic rational Alexander modules endowed with their Blanchfield forms if and only if they can be obtained from one another by a finite sequence of null rational Lagrangian-preserving surgeries, i.e. Lagrangian-preserving surgeries performed on rational homology handlebodies homologically trivial in the complement of the knot. In Chapter 6, we study the graded space associated with the filtration of the rational vector space generated by pairs (M,K) defined by null rational Lagrangian-preserving surgeries. These last two chapters contain work in progress.
identifier: NNT: 2012GRENM071
issued: 2026-05-11T16:26:47.276483
language: fr
modified: 2026-05-11T16:26:47.276493
contact point: Organization
  fn: CCSD
keyword: alexander-module
keyword: blanchfield-form
keyword: borromean-surgery
keyword: chirurgie-borromeenne
keyword: chirurgie-preservant-le-lagrangien
keyword: finite-type-invariants
keyword: forme-de-blanchfield
keyword: infoeu-reposemanticsdoctoralthesis
keyword: invariants-de-type-fini
keyword: lagrangian-preserving-surgery
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: module-dalexander
keyword: rational-homology-spheres
keyword: spheres-dhomologie-rationnelle
keyword: theses
landing page: https://theses.hal.science/tel-00808274

Equivariance and finite type invariants in dimension 3
type: Distribution
format: HTML
issued: 2026-05-11T16:26:47.307287
modified: 2026-05-11T16:26:47.244109
access URL: https://theses.hal.science/tel-00808274

test_moissonnage_selune
type: Agent