Mathematical Sciences: Topology of 4-Dimensional Manifolds

Investigator(s):

Dariusz Wilczynski (PI)

Sponsor:

University of Notre Dame, IN 46556 5746317432

Start Date/Expiration Date

1991-07-01 to 1993-12-31 (amended 1991-07-19)

Awarded Amount to Date:

$42,000

Abstract: The research consists of three projects in the topology of 4-dimensional manifolds. The first project is a continuation of joint work with R. Lee (Yale University) in which the investigations are focused on: (a) the least genus problem for embedded surfaces, (b) obstruction theory for embeddings, and (c) topological rigidity of simple embeddings. The second project concerns finite group actions on 4-manifolds, with emphasis on the question of smoothability and methods of classification. The third project concerns nonorientable 4-manifolds and their exotic smooth structures. Manifolds are very natural geometric objects, being the locally Euclidean ones. Answering questions about four- dimensional manifolds, in particular, may have cosmological significance, for we live in a manifold of three space dimensions and one time-dimension.

NSF Org:

DMS - Division of Mathematical Sciences

Award Number:

9103558

Award Instrument:

Standard Grant

Program Manager:

Ralph M. Krause
DMS Division of Mathematical Sciences
MPS Directorate for Mathematical & Physical Sciences

NSF Program(s):

TOPOLOGY, TOPOLOGY

Field Application(s):

Mathematics, Other nsf.applications NEC

Program Element Code(s):

1267
, 1267