Principal Investigator: F. Reese Harvey
This project has three components. First, push forward singular
connections will be analyzed and their associated characteristic
currents will be determined. Second, the calculus of kernels as
developed by Harvey and Polking will be used to attack new
problems in differential geometry. Third, calibration theory,
introduced by Harvey and Lawson, will be applied to geometric
problems.
In practical geometric problems it is important to distinguish
"local" from"global" information. Here "local" means in the
vicinity of a point while by contrast "global" includes
information such as the distance from, say Washington D.C., to
another place on the surface of the earth. Results of particular
importance for applications are frequently ones where global
information is computed from an assembly of local information.
For example local information alone, involving the amount of
local curvature of a surface can be used to distinguish the
global nature of a ball from the global nature of a inner
tube. This research will develope new instances of this important
procedure.
