Mathematical Research Letters

Volume 30 (2023)

Number 5

Ribbon cobordisms as a partial order

Pages: 1511 – 1519

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n5.a8

Author

Marius Huber (Department of Computational Linguistics, Universität Zürich, Switzerland)

Abstract

We show that the notion of ribbon rational homology cobordism yields a partial order on the set of aspherical 3‑manifolds, thus supporting a conjecture formulated by Daemi, Lidman, Vela–Vick and Wong. Our proof is built on Agol’s recent proof of the fact that ribbon concordance yields a partial order on the set of knots in the 3‑sphere.

Received 8 December 2022

Received revised 25 April 2023

Accepted 6 May 2023

Published 14 May 2024