BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yajit Jain (Brown University) DTSTART:20220502T203000Z DTEND:20220502T213000Z DTSTAMP:20260423T004134Z UID:MITTop/48 DESCRIPTION:Title: Topologically Trivial Families of Smooth h-Cobordisms\nby Yajit Jain ( Brown University) as part of MIT topology seminar\n\n\nAbstract\nAfter usi ng smoothing theory to introduce a notion of exotic smooth structures on m anifold bundles\, we will discuss an equivalent class of objects: smooth b undles of h-cobordisms with a topological trivialization. Using work of Dw yer\, Weiss\, and Williams\, we will associate to such families an invaria nt called the smooth structure class\, which is closely related to the hig her Franz-Reidemeister torsion of Igusa and Klein. We will illustrate two proofs of a duality theorem for the smooth structure class. This theorem g eneralizes Milnor's duality theorem for Whitehead torsion. A consequence o f this result is the rigidity conjecture of Goette and Igusa\, which state s that\, after rationalizing\, stable exotic smoothings of manifold bundle s with closed even dimensional fibers do not exist.\n LOCATION:https://researchseminars.org/talk/MITTop/48/ END:VEVENT END:VCALENDAR