Homotopy motions of surfaces in $3$-manifolds
Geometric Topology
2022-06-03 v4
Abstract
We introduce the concept of a homotopy motion of a subset in a manifold, and give a systematic study of homotopy motions of surfaces in closed orientable 3-manifolds. This notion arises from various natural problems in 3-manifold theory such as domination of manifold pairs, homotopical behavior of simple loops on a Heegaard surface, and monodromies of virtual branched covering surface bundles associated to a Heegaard splitting.
Keywords
Cite
@article{arxiv.2011.05766,
title = {Homotopy motions of surfaces in $3$-manifolds},
author = {Yuya Koda and Makoto Sakuma},
journal= {arXiv preprint arXiv:2011.05766},
year = {2022}
}
Comments
48 pages, 7 figures; final version, to appear in The Quarterly Journal of Mathematics