After reviewing Hatcher's construction of exotic disk bundles, we will introduce the immersed Hatcher construction of Goette and Igusa, a construction of topologically trivial families of smooth h-cobordisms. Using work of Dwyer, Weiss, and Williams we associate to such families an invariant called the smooth structure class, which is closely related to the higher Franz–Reidemeister torsion of Igusa and Klein. We will highlight progress towards computing this invariant using Morse theory, and a resulting duality theorem for the smooth structure class.

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