Table of Contents
What is knot Sliceness?
In knot theory, a “knot” means an embedded circle in the 3-sphere. The 3-sphere can be thought of as the boundary of the four-dimensional ball. A knot. is slice if it bounds a “nicely embedded” 2-dimensional disk D in the 4-ball.
Are there knots in 4D?
Unknotting a knot in 4D A knot is a closed curve in space. It is quite easy to see that in four dimensions, there are no nontrivial knots. You would not be able to tie a shoe in four dimensional space.
Can all knots be untied?
In mathematics, a knot is an embedding of the circle S1 into three-dimensional Euclidean space, R3 (also known as E3). A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot.
What is the Conway knot problem?
In mathematics, in particular in knot theory, the Conway knot (or Conway’s knot) is a particular knot with 11 crossings, named after John Horton Conway. The issue of the sliceness of the Conway knot was resolved in 2020 by Lisa Piccirillo, 50 years after John Horton Conway first proposed the knot.
How old is Lisa Piccirillo?
29
PICCIRILLO, WHO IS 29, grew up in Greenwood, Maine, which has a population of less than 900.
How many different knots are there?
Mikael Vejdemo-Johansson, a mathematician in Stockholm, recently led a small team on a quest to discern how many tie knots are possible. Their results, uploaded to arXiv, say there are 177,147 different ways to tie the knot of a necktie.
Why are there no knots in 4 dimensions?
There are no nontrivial knots that live in four- or higher-dimensional spaces, because if you have four dimensions to work in you can easily untie any knot. There are no nontrivial knots that live in four- or higher-dimensional spaces, because if you have four dimensions to work in you can easily untie any knot.
Is the Conway knot slice?
A knot is said to be slice if it bounds a smooth properly embedded disk in B4. We demonstrate that the Conway knot is not slice. This completes the classification of slice knots under 13 crossings and gives the first example of a non-slice knot which is both topologically slice and a positive mutant of a slice knot.
Who Solved Conway knot?
Lisa Piccirillo
A Tough Knot to Crack. The Conway knot problem confounded mathematicians for more than fifty years. Then Lisa Piccirillo ’13 solved it in less than a week.
Who Solved knot theory?
In 2020, Piccirillo published a mathematical proof in the journal Annals of Mathematics determining that the Conway knot is not a slice knot, answering an unsolved problem in knot theory first proposed over fifty years prior by English mathematician John Horton Conway….
| Lisa Piccirillo | |
|---|---|
| Doctoral advisor | John Luecke |