Geodesic
Lagrangian cobordism. I
Biran, Paul1 ; Cornea, Octav2
1 Department of Mathematics, ETH-Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
2 Department of Mathematics and Statistics, University of Montreal, C.P. 6128 Succ. Centre-Ville Montreal, QC H3C 3J7, Canada
Journal of the American Mathematical Society, Tome 26 (2013) no. 2, pp. 295-340

Voir la notice de l'article provenant de la source American Mathematical Society

We discuss Lagrangian cobordism between Lagrangian submanifolds (in the monotone setting) and we show that Lagrangian Floer and quantum homologies are rigid with respect to this type of cobordism. We also discuss obstructions to cobordism based on properties of Lagrangian quantum homology, relations to Lagrangian surgery, as well as examples of non-isotopic but cobordant Lagrangians. Finally, Lagrangian cobordism is used to structure the respective class of Lagrangians as a category and the results of the paper are interpreted as indicating the existence of a functor defined on this category with values in an appropriate (derived) Fukaya category and which is compatible with the triangulated structure of the target.
DOI : 10.1090/S0894-0347-2012-00756-5

Biran, Paul 1 ; Cornea, Octav 2

1 Department of Mathematics, ETH-Zürich, Rämistrasse 101, 8092 Zürich, Switzerland
2 Department of Mathematics and Statistics, University of Montreal, C.P. 6128 Succ. Centre-Ville Montreal, QC H3C 3J7, Canada 
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Biran, Paul; Cornea, Octav. Lagrangian cobordism. I. Journal of the American Mathematical Society, Tome 26 (2013) no. 2, pp. 295-340. doi: 10.1090/S0894-0347-2012-00756-5

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