Geometry & Topology

A functorial LMO invariant for Lagrangian cobordisms

Dorin Cheptea, Kazuo Habiro, and Gwénaël Massuyeau

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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.

Article information

Geom. Topol., Volume 12, Number 2 (2008), 1091-1170.

Received: 28 March 2007
Accepted: 16 January 2008
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

3-manifold finite-type invariant LMO invariant Kontsevich integral cobordism category Lagrangian cobordism homology cylinder bottom-top tangle Jacobi diagram clasper


Cheptea, Dorin; Habiro, Kazuo; Massuyeau, Gwénaël. A functorial LMO invariant for Lagrangian cobordisms. Geom. Topol. 12 (2008), no. 2, 1091--1170. doi:10.2140/gt.2008.12.1091.

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