2018/01/19 by Mark Pankov, Pankov, Mark, Adam Tyc +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1801.06585
openalex publication_date 2018/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Γ be a triangulation of a connected closed 2-dimensional (not necessarily orientable) surface. Using zigzags (closed left-right paths), for every face of Γ we define the z-monodromy which acts on the oriented edges of this face. There are precisely 7 types of z-monodromies. We consider the following two cases: (M1) the z-monodromy is identity, (M2) the z-monodromy is the consecutive passing of the oriented edges. Our main result is the following: the subgraphs of the dual graph Γ* formed by edges whose z-monodromies are of types (M1) and (M2), respectively, both are forests. We apply this statement to the connected sum of z-knotted triangulations.