Measuring complexity of curves on surfaces
Max Neumann-Coto, Macarena Covadonga Robles Arenas
TL;DR
This paper explores various measures of complexity for curves on surfaces, such as self-intersections, word length, and covering degree, to understand their interrelations.
Contribution
It introduces a comparative analysis of different complexity measures for curves on surfaces, highlighting their connections and differences.
Findings
Relations between self-intersection number and word length
Bounds on covering degrees for embedded lifts
Insights into complexity measures' interdependence
Abstract
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface , including the minimum number of self-intersections, the minimum length of the words representing them in a geometric presentation of , and the minimum degree of the coverings of to which they lift as embeddings.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications