TITLE: Research in algebraic topology
QUESTION [42 upvotes]: I have started studying algebraic topology with the help of Armstrong(Basic), Massey, and Hatcher. If I plan to do research in algebraic topology in future:

What else should I study after completing homology(basic), cohomology(basic) and homotopy theory(basic)?

After completing Hatcher how far I would be (in terms of time and effort) from tackling a research problem?
I have average background in Algebra and never studied Category theory in detail.However I feel comfortable working with algebra. I would like to work in those areas which require more algebraic machinery than any other area and which are more Geometric in flavour.

Are there other areas to which I should switch over to like Geometric topology or algebraic geometry?

REPLY [2 votes]: Despite your comments in the OP, I think you should consider learning basic Category Theory. Category theory is crucial to most of topology, and a lack of knowledge of category theory will seriously cripple your ability to do topological problems and communicate with other topologists. 
Categories for the Working mathematician by Mac Lane, Schapira's lecture notes, and Categories and Sheaves by Kashiwara and Schapira are good resources for this.