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

Suyoung Choi; Yuanxin Guan; Hyeontae Jang; Zhi Lü

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

Algebraic Topology 2026-07-21 v1 Combinatorics

Authors: Suyoung Choi , Yuanxin Guan , Hyeontae Jang , Zhi Lü

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.

Keywords

simplicial spheres toric lifting characteristic maps mod 2 universal complex

Cite

@article{arxiv.2607.18706,
  title  = {On the toric lifting properties for simplicial $3$-spheres},
  author = {Suyoung Choi and Yuanxin Guan and Hyeontae Jang and Zhi Lü},
  journal= {arXiv preprint arXiv:2607.18706},
  year   = {2026}
}

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15 pages