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WINTER MIDWEST TOPOLOGY SEMINAR

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Calvin College, Grand Rapids, Michigan

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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 CP^{2}. The answer to this is not yet known, and instead we ask whether we can find exotic smooth manifolds homeomorphic to CP^{2} # m(–CP^{2}). 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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