Anybody into applying some Math Knot Theory?

Chit Chat
1

I started a little study of mathematical knot theory - especially regarding notation. I did learn Gauss, Extended Gauss, and Dowker-Thistlethwaite notation. I quickly realized the “unknot” matched any ‘real’ knot tied in the bight and ‘sorta’ gave up on "math knot theory’

However, the more I thought about it, I speculated that Indiana University had a really cool mathematical knot site! I am now thinking that all ‘real knots’ could at least perhaps be mapped to a “mutation” of a mathematical knot. Anybody done any work in this area? Here are some links:


https://knotinfo.math.indiana.edu/


https://knotinfo.math.indiana.edu/descriptions/gauss_notation.html


https://knotinfo.math.indiana.edu/descriptions/dt_notation.html

2

How does one map the common bowline (Ashley’s #1010)
into a closed-curve mathematical knot?!
Tough issues . . .

–dl*

3

Indeed it seems to be! I was hoping to find someone sophisticated in “knot theory” to perhaps educate us. Probably if that were practical we would already know it by this time?