A functorial LMO invariant for Lagrangian cobordisms

Details A functorial LMO invariant for Lagrangian cobordisms A functorial LMO invariant for Lagrangian cobordisms

2007-01-10

arxiv.org/abs/math/0701277v2

Geom. Topol. 12 (2008) 1091-1170

Mathematics

Geometric Topology

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

Scientific paper

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.

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