Knot Theory is the study of, as you may have guessed, knots. What are mathematical knots? Mathematical knots are just like the knots you know, but they cannot be untied. So they are a closed curve in 3D space that does not intersect itself.
The main topic of conversation in Knot Theory is how we can tell two knots apart. This is done by knot invariants. With knot invariants we can tell whether two knots are different. The only way to tell whether two knots are topologically the same, is with the Reidemeister moves.
In this book we will study the basics of Knot Theory and see some Braid Theory amongst other topics.
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- Queen, M., On the Jones Polynomial: A Monica Queen Thesis, arXiv:2108.13835, 2021.