Volume 12, issue 2 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 5, 2487–3110
Issue 4, 1865–2486
Issue 3, 1245–1863
Issue 2, 617–1244
Issue 1, 1–616

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
A functorial LMO invariant for Lagrangian cobordisms

Dorin Cheptea, Kazuo Habiro and Gwénaël Massuyeau

Geometry & Topology 12 (2008) 1091–1170
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 2000
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