Pontrjagin classes and higher torsion of sphere bundles

Abstract

By a classical result of Schafer and Kahn ([12], [6]), oriented topological sphere bundles have well defined rational Pontrjagin classes. In the smooth case, we show that the corresponding Pontrjagin character is proportional to the higher Franz-Reidemeister torsion invariant in each degree when the fiber is even dimensional and we discuss the relationship in the odd dimensional case.