What's a somewhat fast introduction to (differential) geometry and algebraic topology for someone who knows a lot of analysis but little else?

Question

I never got to learn much about geometry beyond curves and surfaces in Calculus III, and point set topology.

So what is a fast introduction to differential geometry (specifically, differential manifolds) and algebraic topology? My goal is to learn about Teichmuller surfaces, and I would like to achieve that within a year -- a year and a half.

inb4 there is no royal road to geometry; I just do not want slow textbooks.

Here : http://math.stackexchange.com/questions/13575/teaching-myself-differential-topology-and-differential-geometry — user135520, Aug 29 '15 at 20:10

score 0 · Answer 1 · answered Aug 29 '15 at 17:58

You need to tell us something more. Are you interested in very formal book with all the technicalities or rather something which mostly emphasises ideas and results. Is your background in pure mathematics or rather applications like physics etc. If you would choose second answer to both questions I strongly recommend Frankel, but it's actually a huge book. If you are more in for formality there are three books by Lee - one for differential topology, differential geometry and Riemannian geometry respectively. Then again, if you want to read all three it's a LOT. The reason is that things you mentioned are extremely diverse fields. It might be that you only need a small part of that. In any case, good luck with your goal!

Very good points.
I am interested in a book that emphasizes ideas and results. I come from a background in pure mathematics, but I avoided taking geometry classes throughout my education and now I need to catchup.

Thanks! — , Aug 29 '15 at 18:03

What's a somewhat fast introduction to (differential) geometry and algebraic topology for someone who knows a lot of analysis but little else?

1 Answers1