Regularly slice implies once-stably decomposably slice

TL;DR

This paper explores the relationship between regular and decomposable Lagrangian cobordisms, establishing implications and distinctions, and introduces new concepts and examples in symplectic topology.

Contribution

It proves that regular sliceness implies once-stably decomposable sliceness and demonstrates that regularity is preserved under satelliting, highlighting differences between regularity and decomposability.

Findings

Regular sliceness implies once-stably decomposable sliceness.

Satelliting preserves the regularity of concordance.

Constructs decomposably slice knots that may not be strongly decomposably slice.

Abstract

We investigate the relationship between regular and decomposable Lagrangian cobordisms in $4$-dimensional symplectizations. First, we show that regular sliceness implies once-stably decomposable sliceness, and offer a stabilization-free strategy. On the other hand, we show that satelliting preserves regularity of concordance, suggesting that regularity and decomposability are distinct in general. Among other results, we compare the symplectic and smooth slice-ribbon conjectures and construct decomposably slice knots that may not be strongly decomposably slice.