Alternative versions of the Johnson homomorphisms and the LMO functor

Abstract : Let Σ be a compact connected oriented surface with one boundary component and let M denote the mapping class group of Σ. By considering the action of M on the fundamental group of Σ it is possible to define different filtrations of M together with some homomorphisms on each term of the filtration. The aim of this paper is twofold. Firstly we study a filtration of M introduced recently by Habiro and Massuyeau, whose definition involves a handlebody bounded by Σ. We shall call it the "alternative Johnson filtration", and the corresponding homomorphisms are referred to as "alternative Johnson homomorphisms". We provide a comparison between the alternative Johnson filtration and two previously known filtrations: the original John-son filtration and the Johnson-Levine filtration. Secondly, we study the relationship between the alternative Johnson homomorphisms and the functorial extension of the Le-Murakami-Ohtsuki invariant of 3-manifolds. We prove that these homomorphisms can be read in the tree reduction of the LMO functor. In particular, this provides a new reading grid for the tree reduction of the LMO functor.
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https://hal.archives-ouvertes.fr/hal-02050022
Contributeur : Anderson Vera <>
Soumis le : mardi 26 février 2019 - 18:00:04
Dernière modification le : lundi 11 mars 2019 - 09:18:01

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  • HAL Id : hal-02050022, version 1

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Anderson Vera. Alternative versions of the Johnson homomorphisms and the LMO functor. 2019. 〈hal-02050022〉

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