Abstract:Using the work of Dwyer, Weiss, and Williams we associate an invariant to any topologically trivial family of smooth h-cobordisms. This invariant is called the smooth structure class, and is closely related to the higher Franz-Reidemeister torsion of Igusa and Klein. We compute the smooth structure class in terms of a fiberwise generalized Morse function using fiberwise Poincaré-Hopf theory. This computation gives rise to a duality theorem for the smooth structure class that generalizes Milnor's duality theore… Show more
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