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arXiv · 2607.18706

On the toric lifting properties for simplicial $3$-spheres

Suyoung Choi·Yuanxin Guan·Hyeontae Jang·Zhi Lü
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Abstract

We study the lifting problem for mod $2$ characteristic maps over simplicial $3$-spheres. Using a bad-block partition of the universal complex $X(\mathbb{Z}_2^4)$, we prove an avoidance criterion for liftability. We show that every simplicial $3$-sphere with at most $20$ vertices has the toric lifting property. We also obtain image-size and join-type results, and prove sharpness of the image-size bound in the universal-complex sense.

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Suyoung Choi, Yuanxin Guan, Hyeontae Jang, Zhi Lü. 2026-07-21. On the toric lifting properties for simplicial $3$-spheres. https://arxiv.org/abs/2607.18706

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