2007/01/31 by Dorin Cheptea, Kazuo Habiro, Gwénaël Massuyeau +1 · 28 citations
Mathematics · #Advanced Combinatorial Mathematics #Functor #Geometric and Algebraic Topology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Lagrangian #Singular homology #Universality (dynamical systems) #math.GT #math.QA #msc:57M25 #msc:57M27
paper · pdf · doi:10.2140/gt.2008.12.1091
published in Geometry & Topology 12(2), 1091-1170 (Mathematical Sciences Publishers) · 59 pages with many figures. Some minor changes in the writing, and a few precisions added
arxiv created 2007/03/22 · openalex publication_date 2008/05/24 · arxiv updated 2014/11/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.