Project Details
Description
The PI seeks to understand the algorithmic structure of three-manifolds.
To be precise: the PI will work on the Heegaard genus problem and will
attack the question of computing the Hempel distance of a Heegaard
diagram. Both questions are difficult due to their connections to the
Poincare Conjecture and the three-sphere recognition problem. There are
several existing tools which spring to mind: on the one hand Haken and
Rubinstein's combinatorial theory of normal and almost normal surfaces
while on the other hand there are ideas from the theory of Kleinian
groups, involving the curve complex.
To give the flavor of the algorithmic problems involved consider the
following 'toy' version: your garden hose, lying on the lawn, is very
tangled. You must untangle it before putting it away. Is there a
mechanical procedure (to program into your robot butler) which will
untangle the hose regardless of its starting position? How fast is the
procedure? If the neighbor's child screws the ends of the hose together
can your butler at least manage to straighten the hose into a circle?
Can the butler finish faster if the hose is shorter? How much faster?
Status | Finished |
---|---|
Effective start/end date | 6/15/05 → 5/31/09 |
Funding
- National Science Foundation: $92,751.00