Knot exteriors with all compact surfaces of positive genus essentially embedded
Geometric Topology
2025-08-26 v1
Abstract
It is well known that there exist knots with Seifert surfaces of arbitrarily high genus. In this paper, we show the existence of infinitely many knot exteriors where each of which has longitudinal essential surfaces of any positive genus and any number of boundary components.
Cite
@article{arxiv.2508.17504,
title = {Knot exteriors with all compact surfaces of positive genus essentially embedded},
author = {Joao M. Nogueira},
journal= {arXiv preprint arXiv:2508.17504},
year = {2025}
}
Comments
13 pages, 10 figures. To appear in Topology and its Applications