Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
2  
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
3  
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.