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A
functorial LMO invariant for Lagrangian cobordisms
Dorin Cheptea, Kazuo Habiro and Gwénaël Massuyeau |
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Geometry & Topology 12 (2008) 1091–1170
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Abstract |
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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
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Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25
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References |
Publication
Received: 28 March 2007
Accepted: 16 January 2008
Published: 24 May 2008
Proposed: Peter Teichner
Seconded: Shigeyuki Morita, Rob Kirby
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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 |
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| Kazuo Habiro | |
| Research Institute for Mathematical
Sciences Kyoto University Kyoto 606-8502 Japan |
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| Gwénaël Massuyeau | |
| Institut de Recherche Mathématique
Avancée Université Louis Pasteur – CNRS 7 rue René Descartes 67084 Strasbourg France |
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