Optimal sweepouts of a Riemannian 2-sphere
Differential Geometry
2016-06-28 v3 Geometric Topology
Abstract
Given a sweepout of a Riemannian 2-sphere which is composed of curves of length less than L, we construct a second sweepout composed of curves of length less than L which are either constant curves or simple curves. This result, and the methods used to prove it, have several consequences; we answer a question of M. Freedman concerning the existence of min-max embedded geodesics, we partially answer a question due to N. Hingston and H.-B. Rademacher, and we also extend the results of [CL] concerning converting homotopies to isotopies in an effective way.
Cite
@article{arxiv.1411.6349,
title = {Optimal sweepouts of a Riemannian 2-sphere},
author = {Gregory R. Chambers and Yevgeny Liokumovich},
journal= {arXiv preprint arXiv:1411.6349},
year = {2016}
}
Comments
20 pages, 8 figures; Modified statements and proofs of theorems to reflect changes in "Contracting loops on a Riemmanian 2-surface" by the first author and R. Rotman