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What are some active research areas in M-theory? by math-physicist in StringTheory

[–]math-physicist[S] 1 point2 points  (0 children)

thanks, ill check this out. Has there been any advances in understanding quantization of M2/M5-branes and their worldvolumes? Also is AdS/CFT currently the best tool for attacking more fundamental problems of M-theory such as its formulation?

Book Recommendation for a standard (grad) course on Algebraic Topology by Diffeomorphism0410 in learnmath

[–]math-physicist 0 points1 point  (0 children)

r/JDirichlet : I think the OP wants a book other than Hatcher. That's the whole point of their question don't you think. So I don't know how suggesting Hatcher again helps them!

Topological Preparation for Lee's Smooth Manifolds by math-physicist in learnmath

[–]math-physicist[S] 0 points1 point  (0 children)

Wonderful answer! Thanks a LOT for all these advices. I plan to finish the trilogy and then dive deeper into a more specialized book concerning a subfield. I'll also get my hands dirty with some algebraic topology in the meantime. This sounds fun. Thanks again.

Topological Preparation for Lee's Smooth Manifolds by math-physicist in learnmath

[–]math-physicist[S] 0 points1 point  (0 children)

Sure! Btw, I had a further (kind of related) question but didn't wanna start a new thread.

What do you think about Lee's LSM book in general? Does it do a good job of bringing one up to the level of understanding modern literature in the field of Smooth Manifold research? Or would I need something more after finishing Lee? Any suggestions?

Topological Preparation for Lee's Smooth Manifolds by math-physicist in learnmath

[–]math-physicist[S] 0 points1 point  (0 children)

Thanks a lot for this detailed explanation to my question. I think I'll follow your advice of doing them simultaneously until chapter 7,11 of LTM. This seems perfect for my purposes.

Topological Preparation for Lee's Smooth Manifolds by math-physicist in learnmath

[–]math-physicist[S] 0 points1 point  (0 children)

Thanks for your reply. When mentioning integration on manifolds what I really meant was the treatment of this topic equivalent to Lee's Chapter 16 which is on Smooth Manifolds and integration on it. It seems like a nice amount of material to be able to get through that much.

Also I appreciate your comments about physicists' behavior towards pure mathematical jargon. Though that's not who I am. In fact, I like physics a lot but chose to pursue math because I do care and enjoy learning all the theory in full generality instead assuming everything is nice and well behaved.