On the combinatorics of Murai spheres and its applications
Abstract
We classify the combinatorial types of Murai spheres in dimensions $1$ and $2$, thereby showing that the corresponding convex simple polytopes have Delzant realizations. Then we describe all chordal Murai spheres $\mathrm{Bier}_c(M)$ with $c\in\mathbb N^m$ and $m\leq 2$. Finally, we find all possible values for the Buchstaber and chromatic numbers of arbitrary Murai spheres.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Commutative Algebra and Its Applications
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 February 2026
- Language
- EN
- Document type
- Preprint