A new pair of non-cobordant surface-links which the Orr invariant, the Cochran sequence, the Sato-Levine invariant, and the alinking number cannot find

TL;DR

The paper introduces a novel method to distinguish non-cobordant surface-links that traditional invariants and theorems cannot differentiate, providing new insights into surface-link classification.

Contribution

A new technique for detecting non-cobordant surface-links that surpasses existing invariants and theorems in certain cases.

Findings

Identified a pair of non-cobordant surface-links indistinguishable by traditional invariants.

Developed a new detection method that successfully distinguishes the pair.

Demonstrated the limitations of existing invariants and the effectiveness of the new approach.

Abstract

We submit a new way to detect pairs of non-cobordant surface-links. We find a new example of a pair of non-cobordant surface-links with the following properties: Orr invariant, Cochran sequence, Sato-Levine invariant, the alinking number and one of Stallings's theorems cannot distinguish them. However our new way can distinguish them.