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Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant. (Homomorphismes de Morita infinitésimaux et réduction arborée de l’invariant LMO.) (English. French summary) Zbl 1248.57009
The author studies infinitesimal versions of the $$k^{th}$$ Morita homomorphism by studying actions of mapping classes on Mal’cev Lie algebras of certain nilpotent quotients of the fundamental group of the underlying surface. The author then explores the relationship between the infinitesimal version and the usual version of the Morita homomorphisms.
Finitely, connections to finite-type invariants (such as LMO invariants) are discussed.

##### MSC:
 57M27 Invariants of knots and $$3$$-manifolds (MSC2010) 57R19 Algebraic topology on manifolds and differential topology 57R50 Differential topological aspects of diffeomorphisms 20F28 Automorphism groups of groups 20F38 Other groups related to topology or analysis 20F40 Associated Lie structures for groups
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