Small triangulations of simply connected 4-manifolds

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2025年10月9日

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Jonathan Spreer,
Lucy Tobin

摘要

We present small triangulations of all connected sums of $\mathbb{C}\mathbb{P}^2$ $C P^{2}$ and $S^2 \times S^2$ $S^{2} \times S^{2}$ with the standard piecewise linear structure. Our triangulations have $2\beta _2+2$ $2 β_{2} + 2$ pentachora, where $\beta _2$ $β_{2}$ 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.