The number of smooth 4-manifolds with a fixed complexity
Abstract
Description
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 $n^2$. In this paper we prove that the number of diffeomorphism classes grows at least as fast as $n^{c\sqrt[3]{n}}$. Along the way we construct complete kirby diagrams for a large family of knot surgery manifolds.
Schematics of Kirby diagrams for the knot surgery manifolds were replaced with actual Kirby diagrams, and minor errors were fixed
Schematics of Kirby diagrams for the knot surgery manifolds were replaced with actual Kirby diagrams, and minor errors were fixed