Calvin College, Grand Rapids, Michigan

February 26 and 27, 2005

Speaker: Ron Fintushel

Title: 4-manifolds with b+=1

Time: Saturday, 3:15 - 4:15 p.m.

Abstract: This last year has seen significant progress in understanding 4-manifolds with b+ = 1. A basic question is whether there is a smooth 4-manifold which is homeomorphic but not diffeomorphic to CP2. The answer to this is not yet known, and instead we ask whether we can find exotic smooth manifolds homeomorphic to CP2 # m(–CP2). Up until a year ago m = 8 was the smallest, but now there are examples down to m = 5. I will explain the difficulties associated to 4-manifolds with b+ = 1 and outline some work, joint with Ron Stern, which allows the construction of infinite families of examples.

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