Knot Theory 6: The Knot Group 

This course is a top-grade one! Taught with rigor, enthusiasm and passion. Especially on a set of topics rarely touched in mainstream math. Chapeau,

Seeing how Anthony play with his toys to demonstrate the subtlety of a simple change to unknot the Borromean rings is very exciting and inspiring. If there were more teachers like him in the class there will be less suffering for math students

Thank you very much for posting these lectures!

I'd imagine the creator(s) of this universe are masters at knot theory

Amazing and you made it very easy , thank you very much ❤❤❤

A natural question to ask is if two knots are equivalent iff their complements (as subspaces of ℝ³) are homeomorphic. The ⟹ direction is easy, but I suspect ⟸ is only true up to knot mirroring (unless we consider more structure on the subspaces). Edit: My suspicion is correct for tame knots (e.g. smooth knots or knots with a diagram with finite number of crossings). See the Gordon-Luecke theorem.

This is a wonderful course, thank you for making it! Question: is there a way to construct a knot with a given group in a Wirtinger presentation?

my brain needed to catch up a bit away from normal homotopy and realizing the base point had to be fixed, since it kept being like "but aren't x, y, and z all homotopic loops?"

We have came through knot theory

This was a fabulous lecture....complete with a magic trick at the end. Only suggestion.....you sometimes mention names that are hard to spell just from hearing them. (like the special linked three rings) It would be helpful if you would spell these special names on the board.

Dear professor Anthony Bosman, I'm a highchool student in Korea. At first, thank you for the enthusiastic video. I was really impressed by the high quality and the content of the lecture. I've already knew the concepts of fundamental group and knot theory, but I've never thought of combining both up! And also the physical visualization of abelian and non-abelian fundamental groups were intriguing. In fact, I'm trying to operate a math experience booth in the school festival, so if it's okay, can I use your instance for the experience booth?

Thank you for these great movies! I´m preparing a lesson for my students about knot theory, and I would like to know where you have bought these string that you illustrates the knots with? Kindest regards, teachter from Sweden.

22:45 For a deformation retract, does the map need to be the identity? Could it instead be any homomorphism of X?

Wow❤

What if I have a plane with two pocked holes. Is it ZxZ? Doesn't seem like it because the winding doesn't have a*b = b*a property.

How might you explain to a lay person why gluing the edges of a rectangular sheet of paper to form a torus is permissible? When the "rules" of topology are first given, we say you cannot cut a space and re-glue its components in some odd fashion, because the relative position of points now get changed. But with a rectangular sheet of paper folded to make a torus, separate points on opposing edges end up fusing together, thus altering the relative position of these points. Do we simply tell a lay person that this is permissible to create a new space, whereas the "don't-cut-and-re-glue rule" is meant to preserve a space?

Can you speak about Van Kampen theorem please?

fuzzy math

Never happened. The Japanese were gunned down by British gunboats and then there were two or three crocodiles who ate a few of the dead bodies.