Problems: drive.google.c... We define the knot concordance group and the signature of a knot, a concordance invariant that helps us distinguish knots up to concordance.
This is a really wonderful course. I became interested in knots because I wanted to explore the idea of using them for qualitative analysis of particle systems (e.g. the n-body problem). These lectures were just what I needed to get started.
Hello! I've watched through all of the 12 series of this course several times, patiently "pause and paundering", doing most of the exercises, googling for proofs of elementary-basics you omit and digging through them, and as a result of this I wanna state that this course that you created is unbelievably perfect! Thank You so much for this, I mean, really, this pushed me to another level somehow, "unlocked the door to so much" using your words to express this. You have that rare subtle feeling, the talent for teaching, that golden mean between diving into strict proofs and giving the overall picture, I swear that concordance and 4-th dimension inside an S3 sphere and all that slicing abstraction - that depicted so bright inside my brain, I finally caught that feeling of pure thinking as it seems for me now, that pushed me so far ahead, I swear I feel that deep cuaseless happiness, this is unbelievable, I have never felt something this deep and pure before. If You ever read this, please accept my endless respect for Your skill and eagerness for what You are into, so there are people inspired by what You do here and it's priceless, kindest regards from Russia, I'd greatly appreciate if You could guide me with links to material that I can investigate further to deepen my insight to this beautiful and unexplored-still %) world of mathematics! I also have an idea of maybe creating a course similar to this - ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-fNk_zzaMoSs.html Please have a look at these series of 3blue1brown, those animations and a clever-briefing-down the contents work even more effectively! Maybe You can think of a new course that we can create together, using Your insight and logics and ability to narrow down effectively + my programming skills and overall knowledge of careful information feeding to public - this can perhaps create something very interesting and informative, people's hunger for knowledge is so surprisingly big nowadays, that can lead, with devotion and patiens - to huge results! Feel free to drop a reply for me here so I can contcat You for further cooperation if this is of any interest to You! And finally, once again, Endless thank's for Your work and passion, cheers!!!
Watched all of this and done all the exercises. Lots of fun! I recommend sharing a link for donation in the description or inside the video. Can imagine it takes a lot of resources to make them.
"Capping off" an unknot is the topological operation of identifying the unknot with the boundary of an unknotted disk (in the sense of a quotient space), which always yields an unknotted disk. Similarly, you could "cap off" an unknotted 2-dimensional sphere, which yields a 3-dimensional ball. Intuitively, you're filling in a hole that doesn't contain much information.
