Small Triangulations of Simply Connected 4-Manifolds

Abstract

We present small triangulations of all connected sums of ${\mathbb{CP}}^2$ and $S^2\times S^2$ with the standard piecewise linear structure. Our triangulations have $2{\hat{I}}_2^2+2$ pentachora, where ${\hat{I}}_2^2$ is the second Betti number of the manifold. By a conjecture of the authors and, independently, Burke, these triangulations have the smallest possible number of pentachora for their respective topological types.

28 pages, 6 figures, 8 tables, 8 pages of appendix