Cobordism-equivalence for codimension-one submanifolds
Geometric Topology
2026-05-07 v1
Abstract
We show that two hypersurfaces in a manifold are related by a sequence of embedded cobordisms if and only if they represent the same homology class. By applying handle decompositions we turn these cobordisms into a sequence of embedded surgeries. Specializing to Seifert surfaces we obtain a conceptual proof that two Seifert surfaces of a fixed link are related by tube attachments and tube removals.
Cite
@article{arxiv.2605.04795,
title = {Cobordism-equivalence for codimension-one submanifolds},
author = {Stefan Friedl and Tobias Hirsch and Clayton McDonald and José Pedro Quintanilha and Daniel Zach},
journal= {arXiv preprint arXiv:2605.04795},
year = {2026}
}
Comments
14 pages, 6 figures