A functorial LMO invariant for Lagrangian cobordisms

Abstract

Lagrangian cobordisms are three-dimensional compact oriented cobordisms between once-punctured surfaces, subject to some homological conditions. We extend the Le-Murakami-Ohtsuki invariant of homology three-spheres to a functor from the category of Lagrangian cobordisms to a certain category of Jacobi diagrams. We prove some properties of this functorial LMO invariant, including its universality among rational finite-type invariants of Lagrangian cobordisms. Finally, we apply the LMO functor to the study of homology cylinders from the point of view of their finite-type invariants.

59 pages with many figures. Some minor changes in the writing, and a few precisions added

Cited by in corpus (13)

• Symplectic Jacobi diagrams and the Lie algebra of homology cylinders
• Lagrangian mapping class groups from a group homological point of view
• Tree homology and a conjecture of Levine
• Abelian quotients of the $Y$-filtration on the homology cylinders via the LMO functor
• Splitting formulas for the LMO invariant of rational homology three-spheres
• Generalized Dehn twists on surfaces and homology cylinders
• On the kernel of the surgery map restricted to the 1-loop part
• Alternative versions of the Johnson homomorphisms and the LMO functor
• A non-commutative Reidemeister-Turaev torsion of homology cylinders
• Splitting formulas for the rational lift of the Kontsevich integral
• Homological Construction of Quantum Representations of Mapping Class Groups
• An extension of the LMO functor
• Torsion elements in the associated graded of the $Y$-filtration of the monoid of homology cylinders