The number of smooth 4-manifolds with a fixed complexity
Dave Auckly
Abstract
One can define the complexity of a smooth 4-manifold as the minimal sum of the number of disks, strands and crossings in a Kirby diagram. Martelli proved that the number of homeomorphism classes of complexity less than n grows as n2. In this paper we prove that the number of diffeomorphism classes grows at least as fast as nc[3]n. Along the way we construct complete kirby diagrams for a large family of knot surgery manifolds.
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