The Alexander Polynomial
What are the 3 steps to create an Alexander polynomial out of a knot?
1. Label regions and crossing
2. Create a table using a cheat sheet
3. Find the determinant of the table (matrix)
Who discovered Tricolorabilty?
Ralph Fox
What is the first Reidemeister move?
Pulling on each side of a knot to undo a simple loop
What is the purpose of the Alexander Polynomial?
To figure out the unknotability of a knot
When and where was tricolorability discovered
1956 at Haverford University
What is the second Reidemeister move?
The crossing or un-crossing of two curved pieces of a knot
Who created the Alexander Polynomial
J.W. Alexander
What is Tricolorability?
A knot's ability to be colored using 3 different colors and have various colors at each crossing
What is the third Reidemeister move?
The moving of a horizontal line above or under a crossing
When was the Alexander Polynomial discovered?
1928
Is a knot invariant always tricolorable?
Yes
Who, where, and when were Reidmister's moves discovered
Reidemeister moves were discovered by Kurt Reidemeister in 1927 in Braunschweig, Germany.
Define a complement of a knot (used to craft an Alexander Polynomial)
The complement of a knot in knot theory is everything outside the knot or everything that is “around” the knot
Define a knot invariant (related because tricolorability uses invariants)
An Invariant is a function, quantity, or property that remains unchanged when a specified transformation is applied.
What are Reidmister's moves?
Moves you can use to manipulate a knot to simplify or solve it