2022/01/01 by Denali Relles, Relles, Denali
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2209.04720
openalex publication_date 2022/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
For a compact surface S with a finite set of marked points P , we define a 1-system tobe a collection of arcs which are pairwise non-homotopic and intersect pairwise at mostonce. We prove that, up to equivalence, there are exactly 23 maximal 1-systems on (S, P)when S is a torus and |P | = 2.Along the way, we generalize some of the results of a paper of Przytycki to the context of surfaces withboundary. In particular, we prove that the maximal cardinality of a 1-system on (S, P)is 2|χ|(|χ| + 1) − v/2 , where χ is the Euler characteristic of (S, P) and v is the number ofmarked points of P in the boundary of S