# Whitehead torsion (Ex)

From Manifold Atlas

Show that for the generator is a unit and hence defines an element in . Prove that we obtain a well-defined map

by sending the class represented by the -automorphism to , where is the -linear map

with respect to the -action on given by multiplication with . Finally show that generates an infinite cyclic subgroup in .

This is a detailed version of [Milnor1966, Example 6.6] and [Kreck&Lück2005, Ex 5.4].