Tom Goodwillie

Abstract: Most smooth fiber bundles having closed disks as fibers are exotic in the sense that they do not arise from vector bundles. This has been known since the 1970s, using algebraic K-theory. Allen Hatcher suggested a concrete way of constructing exotic bundles using the space G/O. Kiyoshi Igusa provided an invariant called higher Reidemeister torsion that can detect exotic bundles and showed that it is nontrivial on Hatcher's construction. Goodwillie, Igusa, and Ohrt extended some of these ideas to settings involving manifolds with free cyclic group actions, and Goodwillie and Igusa are working on further generalizations involving arbitrary finite groups and non-free actions.