Overdetermined systems, invariant connections, and short detour complexes

Tuesday, August 1, 2006 - 11:15am - 12:00pm
EE/CS 3-180
A. Rod Gover (University of Auckland)
With mild restrictions, each overdetermined differential operator is
equivalent to a (tractor-type) connection on a prolonged system, and
this connection depends only on the operator concerned. On the other
hand in Riemannian geometry (for example), natural conformally
invariant overdetermined operators may, given suitable curvature
restrictions, be extended to an elliptic conformally invariant complex
that we term a short detour complex. (These complexes yield an
approach to studying deformations of various structures, and these
complexes and their hyperbolic variants also have a role in gauge theory.)
These constructions are intimately related.