Equivalence Relations Between Closed Curves On the Pair of Pants

Nithin Kavi

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arXiv · 1909.13187

Equivalence Relations Between Closed Curves On the Pair of Pants

Nithin Kavi

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Abstract

We examine an equivalence relation between free homotopy classes of closed curves on the pair of pants known as k-equivalence, a generalization of a concept previously defined by Leininger. We prove that two classes of closed curves on the pair of pants that are k-equivalent must also be 1-equivalent and 2-equivalent. We also examine properties of 1-equivalence on the pair of pants in greater depth.

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Nithin Kavi. 2019-09-29. Equivalence Relations Between Closed Curves On the Pair of Pants. https://arxiv.org/abs/1909.13187

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