English

A functorial LMO invariant for Lagrangian cobordisms

Geometric Topology 2014-11-11 v2 Quantum Algebra

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

Cite

@article{arxiv.math/0701277,
  title  = {A functorial LMO invariant for Lagrangian cobordisms},
  author = {Dorin Cheptea and Kazuo Habiro and Gwenael Massuyeau},
  journal= {arXiv preprint arXiv:math/0701277},
  year   = {2014}
}

Comments

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

R2 v1 2026-07-22T17:49:08.642Z