Measuring complexity of curves on surfaces
classification
🧮 math.GT
keywords
minimumsigmacomplexitycurvesclassesconsidercoveringsdegree
read the original abstract
We consider the relations between different measures of complexity for free homotopy classes of curves on a surface $\Sigma$, including the minimum number of self-intersections, the minimum length of the words representing them in a geometric presentation of $\pi_1(\Sigma)$, and the minimum degree of the coverings of $\Sigma$ to which they lift as embeddings.
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