Exotic characteristic classes and their relation to universal surgery classes (Q760044)

Exotic characteristic classes had been defined by \textit{F. P. Peterson} [Adv. Math. 4, 81--90 (1970; Zbl 0189.54402)] and \textit{D. C. Ravenel} [Comment. Math. Helv. 47, 421--436 (1972; Zbl 0258.55008)] by means of twisted secondary cohomology operations applied to the Thom class of a spherical fibration.The crucial point in their definition was a certain indeterminacy. In the present paper the authors define unique exotic characteristic classes and show that these are related to well-known obstruction classes constructed by Madsen-Milgram and Brumfield-Morgan.