The main purpose of this research project is to study symmetries of manifolds, with particular attention paid to symmetries of 4-dimensional manifolds. The problems to be studied vary from general questions concerning the geometric structure of exotic space forms and 4-dimensional manifolds to many specific problems connected with the existence of symmetric and asymmetric manifolds. The broad spectrum of methods which will be employed in this research include the techniques of surgery and homotopy theory, transformation groups, differential geometry and gauge theory. Since manifolds are very natural geometric objects, including spheres and tori, for example, and since symmetry is a very natural geometric property, techniques for treating symmetry of manifolds are important to cultivate.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
8901583
Program Officer
Ralph M. Krause
Project Start
Project End
Budget Start
1989-06-15
Budget End
1991-11-30
Support Year
Fiscal Year
1989
Total Cost
$47,450
Indirect Cost
Name
Tulane University
Department
Type
DUNS #
City
New Orleans
State
LA
Country
United States
Zip Code
70118