TITLE: Normal invariants
QUESTION [7 upvotes]: I am having a hard time finding examples of computations of normal invariants of surgery theory (or more generally the set of homotopy classes of maps $[X,G/O]$). Does anybody have good references?

REPLY [4 votes]: If you want specifically low-dimensional calculations, the Kirby-Taylor article A survey of 4-manifolds through the eyes of surgery does this for 4-manifolds. The discussion highlights the difference between the topological and smooth (= PL in this dimension) cases.