Single self-intersection words on the once-punctured torus and their counting

2024/04/14 by David Fisac, Fisac, David, Mingkun Liu +1
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Geometric and Algebraic Topology #Computational Geometry and Mesh Generation

paper · pdf · doi:10.48550/arxiv.2404.09372

Abstract

We classify closed curves on a once-punctured torus with a single selfintersection from a combinatorial perspective. We then use the classification to determine the number of closed curves with given word-length and with zero, one, and arbitrary self-intersections.

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