The number of smooth 4-manifolds with a fixed complexity

Dave Auckly

The number of smooth 4-manifolds with a fixed complexity

Geometric Topology 2007-06-18 v2

Authors: 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 $n^2$ . 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.

Keywords

smooth 4-manifolds exotic manifolds manifolds

Cite

@article{arxiv.math/0701269,
  title  = {The number of smooth 4-manifolds with a fixed complexity},
  author = {Dave Auckly},
  journal= {arXiv preprint arXiv:math/0701269},
  year   = {2007}
}

Comments

Schematics of Kirby diagrams for the knot surgery manifolds were replaced with actual Kirby diagrams, and minor errors were fixed

The number of smooth 4-manifolds with a fixed complexity

Abstract

Keywords

Cite

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