Small Triangulations of Simply Connected 4-Manifolds

Jonathan Spreer; Lucy Tobin

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arXiv · 2501.18933

Small Triangulations of Simply Connected 4-Manifolds

Jonathan Spreer·Lucy Tobin

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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 $2\beta_2+2$ pentachora, where $\beta_2$ 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.

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Jonathan Spreer, Lucy Tobin. 2025-01-31. Small Triangulations of Simply Connected 4-Manifolds. https://arxiv.org/abs/2501.18933

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