symbol of a differential operator
For a smooth manifold, a vector bundle and a differential operator on sections of , its symbol is the bundle morphism
given at any point on a cotangent vector of the form by
where in the commutator on the right we regard multiplication by as an endomorphism of .
The symbol may naturally be thought of as an element in the K-theory of (Freed).
For instance chapter 2.5 of
Nigel Higson, John Roe, Lectures on operator K-theory and the Atiyah-Singer Index Theorem (pdf)
Dan Freed, Geometry of Dirac operators (pdf)
Revised on April 10, 2013 22:00:48
by Urs Schreiber