2023/11/07 by Gaiane Panina, Panina, Gaiane, Maksim Turevskii +1
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2311.04214
openalex publication_date 2023/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A triangulation of a circle bundle E \xrightarrow[]π B is a triangulation of the total space E and the base B such that the projection π is a simplicial map. In the paper we address the following questions: Which circle bundles can be triangulated over a given triangulation of the base? What are the minimal triangulations of a bundle? A complete solution for semisimplicial triangulations was given by N. Mnëv. Our results deal with classical triangulations, that is, simplicial complexes. We give an exact answer for an infinite family of triangulated spheres (including the boundary of the 3-simplex, the boundary of the octahedron, the suspension over an n-gon, the icosahedron). For the general case we present a sufficient criterion for existence of a triangulation. Some minimality results follow straightforwadly.