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Nov 21, 2009 at 21:41 comment added Ryan Budney This is a special case of Reid Barton's example. It's the Hurewicz-Serre "killing homotopy groups" technique. You kill the first non-trivial homotopy group, and turn the map X' --> X into a fibration. It's a standard technique to compute homotopy groups of spheres and appears in many algebraic topology textbooks.
Nov 21, 2009 at 15:40 history edited Somnath Basu CC BY-SA 2.5
improved LaTeX
Nov 21, 2009 at 8:02 history answered Somnath Basu CC BY-SA 2.5