#### Volume 12, issue 2 (2008)

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A functorial LMO invariant for Lagrangian cobordisms

### Dorin Cheptea, Kazuo Habiro and Gwénaël Massuyeau

Geometry & Topology 12 (2008) 1091–1170
##### 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.

##### Keywords
3-manifold, finite-type invariant, LMO invariant, Kontsevich integral, cobordism category, Lagrangian cobordism, homology cylinder, bottom-top tangle, Jacobi diagram, clasper
Primary: 57M27
Secondary: 57M25