# Normal invariants and G/O (Ex)

From Manifold Atlas

The aim of these exercises is to follow the proof of [Lück2001, Theorem 3.45].

Given the map , define to be the homotopy fibre of :

In [Lück2001, p. 66] there is defined a group of stable fibre homotopy trivialisations of smooth vector bundles over a space which is denoted .

**Exercise 0.1.**
Show that for any space there is a bijection