Scharlemann will apply new 3-manifold techniques arising from the theory of sutured manifolds and graph-theoretic combinatorics to a variety of open problems in knot and link theory, including the additivity of unknotting number and thecabling conjecture. His students will work on related problems. The topological classification of surfaces is a classical matter, depending basically on how many holes they have. The corresponding problem in one higher dimension is vastly more complicated and an active subject of current research by numerous geometric topologists, including Scharlemann and his students.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Application #
8901065
Program Officer
Ralph M. Krause
Project Start
Project End
Budget Start
1989-07-01
Budget End
1992-06-30
Support Year
Fiscal Year
1989
Total Cost
$144,630
Indirect Cost
Name
University of California Santa Barbara
Department
Type
DUNS #
City
Santa Barbara
State
CA
Country
United States
Zip Code
93106