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Invariants de type fini des cylindres d'homologie et des string links

Abstract : The Goussarov-Habiro finite type invariants theory for 3-manifolds with links comes equipped with a topological calculus toolbox called calculus of claspers. In this thesis, we explicitely compute the invariants in low degree for certain classes of objets, by using a so-called graphical method. We study homology cylinders over a surface with 0 or 1 boundary component and framed string links in homology balls. Their degree 1 invariants are characterized in terms of classical invariants, and a correspondance between these two cases is established. We also consider Vassiliev invariants for string links, from the clasper point of view. The computation of degree 2 invariants implies the construction of a certain 2-component string link invariant. Using this, the relationship between Vassiliev and Goussarov-Habiro invariants is studied in the string link case.
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Contributor : Jean-Baptiste Meilhan <>
Submitted on : Thursday, January 15, 2004 - 5:01:18 PM
Last modification on : Monday, March 25, 2019 - 4:52:05 PM
Long-term archiving on: : Wednesday, September 12, 2012 - 12:25:17 PM


  • HAL Id : tel-00004184, version 1



Jean-Baptiste Meilhan. Invariants de type fini des cylindres d'homologie et des string links. Mathématiques [math]. Université de Nantes, 2003. Français. ⟨tel-00004184⟩



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