A closed aspherical manifold is a compact connected manifold whose universal cover is contractible. Let M and N be closed aspherical manifolds, and let F be an isomorphism of their fundamental groups. Borel conjectured that F is always induced by a homeomorphism f of the manifolds. The investigator, in collaboration with L. E. Jones of SUNY-Stony Brook, intends to try to settle this conjecture. Partial results by the investigator and Jones were the main results of the previous N.S.F. grant (DMS-8801312). The project also relates to problems in differential geometry and algebraic K-theory; e.g., does Wh(G) vanish for every torsion-free group G? Manifolds are locally Euclidean spaces, which makes them very natural objects of study. For example, the physical world in which we live has three space dimensions and (in some contexts) a time dimension, making it either a three-dimensional or four-dimensional manifold. Thus the instant project to understand better the structure of manifolds might even have cosmological significance.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
9103743
Program Officer
Ralph M. Krause
Project Start
Project End
Budget Start
1991-07-15
Budget End
1994-06-30
Support Year
Fiscal Year
1991
Total Cost
$135,900
Indirect Cost
Name
Suny at Binghamton
Department
Type
DUNS #
City
Binghamton
State
NY
Country
United States
Zip Code
13902