A functorial LMO invariant for Lagrangian cobordisms

Dorin Cheptea (1) , Kazuo Habiro (2) , Gwenael Massuyeau (3)

1 CTQM - Center for the Topology and Quantization of Moduli Spaces
2 RIMS - Research Institute of Mathematical Sciences
3 IRMA - Institut de Recherche Mathématique Avancée

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.

Domaines: Topologie géométrique [math.GT]; Algèbres quantiques [math.QA]

Dorin Cheptea, Kazuo Habiro, Gwenael Massuyeau. A functorial LMO invariant for Lagrangian cobordisms. Geometry and Topology, 2008, 12, pp.1091-1170. ⟨hal-00135215⟩