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My Geometry and Topology Roadmap - by Vishal Prasad

vishalblog.substack.com · 763 words · saved by 1 readers

Last year I became fascinated with the low-dimensional topologist Bill Thurston. Whenever he would lecture about something that I could understand, I would get this overwhelming sense that topology is filled with magic (of the Alice in Wonderland type). A wonderful example of this is this short video called “Knots to Narnia”: In the 1980s, Thurston circulated a set of lecture notes for his graduate students. It is filled with the bizarre and the arcane. I very much would like to be able to study Thurston’s notes. I’m currently studying some math at the Open University. In the best-case scenario, in two years I’ll get to study a tiny amount of topology. This is very unfortunate. Measure theory and Group Theory are all very nice (and will of course prove helpful in my topological journey), but I do not think I’ll get to study Thurston’s work this side of the intelligence explosion unless I set some very clear intentions for myself now. To that end, I’m assembling a little road map here o

Last year I became fascinated with the low-dimensional topologist Bill Thurston. Whenever he would lecture about something that I could understand, I would get this overwhelming sense that topology is filled with magic (of the Alice in Wonderland type). A wonderful example of this is this short video called “Knots to Narnia”: In the 1980s, Thurston circulated a set of lecture notes for his graduate students. It is filled with the bizarre and the arcane. The twisted jungle gym. This assemblage is in Nil geometry, a twisted Euclidean space. In normal Euclidean space, all these bars meet at…

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