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Lectures on special Lagrangian submanifolds. (English) Zbl 1079.14522
Vafa, Cumrun (ed.) et al., Winter school on mirror symmetry, vector bundles and Lagrangian submanifolds. Proceedings of the winter school on mirror symmetry, Cambridge, MA, USA, January 1999. Providence, RI: American Mathematical Society (AMS); Somerville, MA: International Press (ISBN 0-8218-2159-8/pbk). AMS/IP Stud. Adv. Math. 23, 151-182 (2001).
Summary: These notes consist of a study of special Lagrangian submanifolds of Calabi-Yau manifolds and their moduli spaces. The particular case of three dimensions, important in string theory, allows us to introduce the notion of gerbes. These offer an appropriate language for describing many significant features of the Strominger-Yau-Zaslow approach to mirror symmetry.
For the entire collection see [Zbl 0980.00027].

MSC:
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
53C38 Calibrations and calibrated geometries
32Q25 Calabi-Yau theory (complex-analytic aspects)
53D12 Lagrangian submanifolds; Maslov index
55R65 Generalizations of fiber spaces and bundles in algebraic topology
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