9531964 Kronheimer The proposed research deals with geometry and gauge theory in dimensions three and four, with an emphasis on the study of the monopole equations recently introduced by Seiberg and Witten. These equations have been used to define new differential invariants of manifolds, and the investigator wishes to examine these invariants in isolation as well as in the presence of various geometric structures on the underlying manifold. In addition, the proposed research seeks to understand the internal structure of these invariants in relation to other closely related invariants such as Donaldson invariants. The study of four dimensional curved spaces has received a boost in recent years due to ideas coming from theoretical physics. In the early eighties Donaldson came up with a set of differential invariants (these are used to distinguish and classify different four dimensional spaces) using ideas from particle physics; in 1994 Witten and Seiberg came up with another set of invariants which are considerably easier to calculate.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9531964
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
1996-06-01
Budget End
2002-05-31
Support Year
Fiscal Year
1995
Total Cost
$360,000
Indirect Cost
Name
Harvard University
Department
Type
DUNS #
City
Cambridge
State
MA
Country
United States
Zip Code
02138