Stellar subdivisions, wedges and Buchstaber numbers

Choi, Suyoung; Jang, Hyeontae

doi:10.2140/agt.2026.26.751

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Stellar subdivisions, wedges and Buchstaber numbers

Suyoung Choi and Hyeontae Jang

Algebraic & Geometric Topology 26 (2026) 751–759

DOI: 10.2140/agt.2026.26.751

Abstract

The Buchstaber number of a simplicial complex $K$ is a significant invariant in toric topology. In particular, when $K$ is a (polytopal) PL sphere, the maximal Buchstaber number is closely connected to several important objects, such as toric manifolds, quasitoric manifolds, and topological toric manifolds. A PL sphere is called a seed if it cannot be obtained from another PL sphere through a wedge operation. The toric colorable seed inequality, established by Choi and Park in 2017, bounds the maximal number of vertices of a seed with a maximal Buchstaber number. This inequality plays a key role in characterizing PL spheres that achieve maximal Buchstaber numbers.

We prove that the inequality is tight. Specifically, we show how to construct larger seeds from existing ones using stellar subdivisions and wedges, while preserving both the maximality of Buchstaber numbers and polytopality.

Keywords

Buchstaber number, stellar subdivision, wedge operation, toric topology, inequality

Mathematical Subject Classification

Primary: 57S12

Secondary: 14M25

References

Publication

Received: 16 October 2024

Revised: 17 January 2025

Accepted: 4 March 2025

Published: 11 February 2026

Authors

Suyoung Choi
Department of Mathematics Ajou University Suwon South Korea

Hyeontae Jang
School of Mathematics Korea Institute for Advanced Study Seoul South Korea

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Volume 26, issue 2 (2026)