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The first Pontryagin class

Published online by Cambridge University Press:  20 September 2007

Paul Bressler
Paul Bressler
Affiliation:
School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA bressler@math.ias.edu
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Abstract

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We give a natural obstruction theoretic interpretation to the first Pontryagin class in terms of Courant algebroids. As an application we calculate the class of the stack of algebras of chiral differential operators. In particular, we establish the existence and uniqueness of the chiral de Rham complex.

Keywords

Courant algebroidvertex algebroidgerbechiral differential operators14F10 (primary)57N65 (secondary)
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 5 , September 2007 , pp. 1127 - 1163
Copyright
Foundation Compositio Mathematica 2007