2022/01/04 by Navnath Daundkar, Daundkar, Navnath, Priyavrat Deshpande +1
Computer Science · Mathematics · Physics and Astronomy · #55M30 #55P15 #57R42 #Advanced Combinatorial Mathematics #Advanced Mathematical Theories and Applications #Algebraic Topology (math.AT) #Computational Geometry and Mesh Generation #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2201.01063
openalex publication_date 2022/01/04 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Donald Davis initiated the study of an n-dimensional analogue of the Klein bottle. This generalized Klein bottle occurs as a moduli space of planar polygons for a certain choice of side lengths. In this paper, we show that the n-dimensional Klein bottle is a real Bott manifold and determine the corresponding Bott matrix. We determine the small cover structure on two other classes of moduli spaces of planar polygons. As an application, we compute the rational Betti numbers of these spaces using a formula, due to Suciu and Trevisan.