Learn Differential Topology: Point-Set, Algebraic, & Calculus on Manifolds

[leon1127]

I have just found that topology is very interesting. I just want to know how one studies topology. do they go in the order of Point-set Topology, Algebraic Topology, then Differential Topology? My ultimate goal is to understand Calculus on Manifolds and Morse Theory. Is it possible to jump to Differential Topology with knowledge of basic point-set topology and differential forms?

Thx

 

[slearch]

This is the order one usually does it in. I can't imagine skipping Algebraic Topology - there are too many key things there and there is a large interplay between it and differential forms.

 

[leon1127]

This is the order one usually does it in. I can't imagine skipping Algebraic Topology - there are too many key things there and there is a large interplay between it and differential forms.

thx.
but of course when i say skip it does not mean skip it completely, I will also study the key results of it, however if I want to study the part main related to analysis, is it possible to skip the "non-manifold" related part? The possiblility that i have right now is independent study with a topologist, I just wish to learn the most from him that would help me in further study in calculus of variations.