Exotic Smooth Structures on Topological Fibre Bundles
نویسندگان
چکیده
We use a variation of Hatcher’s construction to construct, rationally stably, all exotic smooth structures on smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension q plus 3). We show that, rationally stably, such smooth structures are classified by a cohomology class in the total space and the relative higher Igusa-Klein (IK) torsion is equal to the push-down of the cohomology class. This answers the question, in the relative case, of which cohomology classes can occur as relative higher torsion classes.
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