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ISSN (electronic): 1364-0380
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A functorial LMO invariant for Lagrangian cobordisms

Dorin Cheptea, Kazuo Habiro and Gwénaël Massuyeau

Geometry and Topology 12 (2008) 1091–1170

DOI: 10.2140/gt.2008.12.1091

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

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M25

References
Publication

Received: 28 March 2007
Accepted: 16 January 2008
Published: 24 May 2008
Proposed: Peter Teichner
Seconded: Shigeyuki Morita, Rob Kirby

Authors
Dorin Cheptea
Previous address: Center for the Topology and Quantization of Moduli Spaces
University of Aarhus
Bygning 1530
Ny Munkegade
8000 Aarhus C
Denmark
Current address: Institute of Mathematics of the Romanian Academy
PO Box 1-764
Bucharest
RO - 014700
Romania
Kazuo Habiro
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan
Gwénaël Massuyeau
Institut de Recherche Mathématique Avancée
Université Louis Pasteur – CNRS
7 rue René Descartes
67084 Strasbourg
France