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Apr 24, 2010 at 21:21 comment added Tim Perutz There are two ways of setting up obstruction theory - an abstract approach using Postnikov towers, and a more concrete one using cell complexes. The second method is the one that I find easier to remember and apply to manifolds. Hatcher covers the first approach nicely; for the second, I think I read Milnor-Stasheff and Steenrod's classic on fibre bundles. (Other MO-ers may have better suggestions...)
Apr 24, 2010 at 18:53 comment added j.c. Can you recommend some good obstruction theory references so that I can learn to work out the calculations you describe? I am still slowly working my way through Hatcher's algebraic topology book; maybe what you mention is in there in a form I can't quite grasp yet?
Apr 22, 2010 at 23:12 vote accept j.c.
Feb 7, 2010 at 17:35 history answered Tim Perutz CC BY-SA 2.5