The principal investigator will analyze how topology determines geometry in several settings. He will study deformation theory for open 3-manifolds, geometrization of automorphisms of free groups, and parallels between renormalization theory and hyperbolic 3-manifolds which asymptotically fiber over a circle. A central theme in modern dynamical systems is the restriction topology puts on allowable dynamics and geometry. For example, on the surface of a sphere, every vector field must have a singularity. On the earth, this means that the wind cannot blow everywhere at once; there must be at least one spot where the air does not move. In this vein, the principal investigator will develop relationships between complex dynamics and the geometry of three-dimensional hypersurfaces.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9016023
Program Officer
James Glazebrook
Project Start
Project End
Budget Start
1990-07-01
Budget End
1993-06-30
Support Year
Fiscal Year
1990
Total Cost
$81,800
Indirect Cost
Name
University of California Berkeley
Department
Type
DUNS #
City
Berkeley
State
CA
Country
United States
Zip Code
94704