Compositio Mathematica

The first Pontryagin class

Paul Bressler a1
a1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA

Article author query
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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.

(Received January 10 2006)
(Accepted October 24 2006)

Key Words: Courant algebroid; vertex algebroid; gerbe; chiral differential operators.

Maths Classification

14F10 (primary); 57N65 (secondary).