Unsolved Problems
Showing 1-7 of 7 problems
Category
Problem Set
Status
TOP-002
Open
The Volume Conjecture
For a hyperbolic knot $K$, the limit of normalized colored Jones polynomials equals the hyperbolic volume of the knot complement....
L4
298
17
DARPA-009
Open
Physical Consequences of Perelman's Proof
Apply Perelman's proof of the Poincaré conjecture to materials fabrication across scales....
L4
267
15
TOP-001
Open
Unknotting Problem
Can unknots be recognized in polynomial time?...
L4
334
27
TOP-002
Open
Berge Conjecture
Are Berge knots the only knots in S³ admitting lens space surgeries?...
L4
167
13
TOP-006
Open
Unknotting Problem
Can unknots be recognized in polynomial time?...
L4
256
20
TOP-008
Open
Whitehead Conjecture
Is every connected subcomplex of a 2-dimensional aspherical CW complex also aspherical?...
L4
143
11
TOP-009
Open
Zeeman Conjecture
Is $K \times [0,1]$ collapsible for every finite contractible 2-dimensional CW complex K?...
L4
134
10