Equivalence Relations Between Closed Curves On the Pair of Pants
Geometric Topology
2019-10-01 v1
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.
Cite
@article{arxiv.1909.13187,
title = {Equivalence Relations Between Closed Curves On the Pair of Pants},
author = {Nithin Kavi},
journal= {arXiv preprint arXiv:1909.13187},
year = {2019}
}
Comments
17 pages, 10 figures