Whitehead torsion

In 1935, Reidemeister, Franz and de Rham introduced the concept of "torsion" for certain finite simplicial complexes. For example let X be a finite complex whose fundamental group TTIX is cyclic of order m. We can identify TT with the group of covering transformations of the universal covering complex X. If ir operates trivially on the rational homology H* (X\ @), then the torsion of X is defined as a certain collection of elements in the algebraic number field Q exp (27ri/m). This torsion is a kind of determinant which describes the way in which the simplexes of X are fitted together with respect to the action of ir. The actual definition will be given in 8. (See Franz [1935