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?



Normal invariants
Many examples of computations of $[M,G/O]$ appear in papers which apply surgery theory. Here are some examples:


* [Brumfiel](https://www.maths.ed.ac.uk/%7Ev1ranick/papers/brumfiel.pdf) did the complex projective spaces $\mathbb{C}P^n$.
* [Land](http://markus-land.de/app/download/2771195/Normal+invariants.pdf) did the complex projective space $\mathbb{C}P^2$.
* [Kirby-Siebenmann](https://www.maths.ed.ac.uk/%7Ev1ranick/papers/ks.pdf) did high-dimensional tori in Appendix V.B.
* [Crowley](https://link.springer.com/article/10.1007/s10711-010-9513-8) did products of spheres $S^p \times S^q$ for $p,q \geq 2$ and $p+q \geq 5$.


