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https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-knot-problem-20200519/
Quanta magazine
KNOT THEORY
Graduate Student Solves Decades-Old Conway Knot Problem
(抜粋)
It took Lisa Piccirillo less than a week to answer a long-standing question about a strange knot discovered over half a century ago by the legendary John Conway.
https://d2r55xnwy6nx47.cloudfront.net/uploads/2020/05/Lisa-Piccirillo_2880_Lede.jpg

Lisa Piccirillo’s solution to the Conway knot problem helped her land a tenure-track position at the Massachusetts Institute of Technology.

n the summer of 2018, at a conference on low-dimensional topology and geometry, Lisa Piccirillo heard about a nice little math problem. It seemed like a good testing ground for some techniques she had been developing as a graduate student at the University of Texas, Austin.

“I didn’t allow myself to work on it during the day,” she said, “because I didn’t consider it to be real math. I thought it was, like, my homework.”

The question asked whether the Conway knot ? a snarl discovered more than half a century ago by the legendary mathematician John Horton Conway ? is a slice of a higher-dimensional knot.
“Sliceness” is one of the first natural questions knot theorists ask about knots in higher-dimensional spaces, and mathematicians had been able to answer it for all of the thousands of knots with 12 or fewer crossings ? except one. The Conway knot, which has 11 crossings, had thumbed its nose at mathematicians for decades.

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