Infinitesimal Morita homomorphisms and the tree-level of the LMO invariant

DOI10.24033/bsmf.2625zbMath1248.57009arXiv0809.4629OpenAlexW1585679613MaRDI QIDQ2883362

Gwénaël Massuyeau

Publication date: 10 May 2012

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0809.4629

zbMATH Keywords

finite-type invariantMagnus expansionTorelli groupJohnson homomorphismshomology cylinderMorita homomorphismsLMO invariantMal'cev Lie algebra

Mathematics Subject Classification ID

Other groups related to topology or analysis (20F38) Automorphism groups of groups (20F28) Associated Lie structures for groups (20F40) Algebraic topology on manifolds and differential topology (57R19) Differential topological aspects of diffeomorphisms (57R50)

Related Items

Abelian quotients of the \(Y\)-filtration on the homology cylinders via the LMO functor ⋮ Cocycles of nilpotent quotients of free groups ⋮ Triviality of the 𝐽₄-equivalence among homology 3-spheres ⋮ Torelli group, Johnson kernel, and invariants of homology spheres ⋮ A non-commutative Reidemeister-Turaev torsion of homology cylinders ⋮ Surgery equivalence relations for 3-manifolds ⋮ The Goldman-Turaev Lie bialgebra in genus zero and the Kashiwara-Vergne problem ⋮ Formality and finiteness in rational homotopy theory ⋮ Canonical extensions of Morita homomorphisms to the Ptolemy groupoid ⋮ Morita’s trace maps on the group of homology cobordisms ⋮ Alternative versions of the Johnson homomorphisms and the LMO functor ⋮ Taylor expansions of groups and filtered-formality ⋮ Finite type invariants and fatgraphs ⋮ Cup products, lower central series, and holonomy Lie algebras ⋮ The Kontsevich integral for bottom tangles in handlebodies ⋮ The geometric intersection number of simple closed curves on a surface and symplectic expansions of free groups ⋮ Generalized Johnson homomorphisms for extended N-series ⋮ Fox pairings and generalized Dehn twists ⋮ Generalized Dehn twists on surfaces and homology cylinders ⋮ Intersection of curves on surfaces and their applications to mapping class groups ⋮ Johnson–Levine homomorphisms and the tree reduction of the LMO functor ⋮ Goldman-Turaev formality implies Kashiwara-Vergne ⋮ Milnor-Orr invariants from the Kontsevich invariant ⋮ Pointed harmonic volume and its relation to the extended Johnson homomorphism ⋮ Formality properties of finitely generated groups and Lie algebras ⋮ Johnson-Morita theory in mapping class groups and monoids of homology cobordisms of surfaces ⋮ THE GENERALIZED DEHN TWIST ALONG A FIGURE EIGHT

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Labeled binary planar trees and quasi-Lie algebras
• A functorial LMO invariant for Lagrangian cobordisms
• Canonical extensions of the Johnson homomorphisms to the Torelli groupoid
• Iterations and logarithms of formal automorphisms
• Abelian quotients of subgroups of the mapping class group of surfaces
• On a universal perturbative invariant of 3-manifolds
• Calculus of clovers and finite type invariants of 3-manifolds
• The Kontsevich integral and Milnor's invariants
• On the Vassiliev knot invariants
• The Århus integral of rational homology 3-spheres. I: A highly non trivial flat connection on \(S ^3\)
• The Århus integral of rational homology 3-spheres. II: Invariance and universality
• Addendum and correction to: ``Homology cylinders: an enlargement of the mapping class group
• Claspers and finite type invariants of links
• Extending Johnson's and Morita's homomorphisms to the mapping class group
• Homology cylinders and the acyclic closure of a free group.
• Bordism invariants of the mapping class group
• Homology and central series of groups
• Rational homotopy theory
• On the associated graded ring of a group ring
• Dehn surgery equivalence relations on 3-manifolds
• A survey of the Torelli group
• Rational cohomology of nilpotent groups and lie algebras
• Finite type invariants and n-equivalence of 3-manifolds
• VASSILIEV HOMOTOPY STRING LINK INVARIANTS
• The Group Ring Of a Class Of Infinite Nilpotent Groups
• Excision in algebraic \(K\)-theory
• Links, pictures and the homology of nilpotent groups