Ribbon cobordisms between lens spaces

TL;DR

This paper characterizes when ribbon rational homology cobordisms exist between lens spaces, showing that only certain lens spaces admit such cobordisms, and applies this to classify ribbon concordances between 2-bridge links.

Contribution

It provides a complete characterization of ribbon rational homology cobordisms between lens spaces and classifies ribbon chi-concordances between connected sums of 2-bridge links.

Findings

A lens space admits a ribbon cobordism to a different lens space only if it is homeomorphic to L(n,1).

Classified ribbon chi-concordances between connected sums of 2-bridge links.

Built on Lisca's work on embeddings of linear lattices.

Abstract

We determine when there exists a ribbon rational homology cobordism between two connected sums of lens spaces, i.e. one without $3$-handles. In particular, we show that if a lens space $L$ admits a ribbon rational homology cobordism to a different lens space, then $L$ must be homeomorphic to $L(n,1)$, up to orientation-reversal. As an application, we classify ribbon $\chi$-concordances between connected sums of $2$-bridge links. Our work builds on Lisca's work on embeddings of linear lattices.