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I'm studying algebraic topology without studying mathematics.

I am familiar with the concepts of fundamental groups, coverings, homology theory, cohomology theory, homotopy theory and cohomotopy theory.

What is/are the next "canonical" topic(s) I should study.

Please don't tell me "just" a topic, because then I could use wikipedia. I need a topic, that can be studied by someone who is just reading a good book or lecture notes.

Thanks for your help.

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Could you clarify what you mean by "studying algebraic topology without studying mathematics"? I ask because "studying algebraic topology" strikes me as studying a domain encompassed within mathematics. –  amWhy Jul 31 '13 at 11:35
Studying algebraic topology without studying mathematics sounds like playing soccer without doing sports. –  azimut Jul 31 '13 at 11:35
I'm reading algebraic topology books and websites, but I'm not studying mathematics at a university. –  Mebat Jul 31 '13 at 11:38
Okay, thanks, @Mebat: So you're self-studying algebraic topology, while not officially enrolled in a mathematics degree program. We have many self-studying students who are doing serious math apart from a formal program of study. Welcome. –  amWhy Jul 31 '13 at 11:41
It depends a bit on what you've already done from the topics you mention, but some suggestions (the first ones to spring to mind at the moment) would be fibre bundles/ characteristic classes, simplicial sets. –  HSN Jul 31 '13 at 12:49

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