Concordances from the standard surface in $S^2\times S^2$

TL;DR

This paper constructs concordances between the standard surface in $S^2\times S^2$ and any homologous surface by combining recent theorems and constructions in 4-dimensional topology.

Contribution

It introduces a method to connect the standard surface to any homologous surface in $S^2\times S^2$ using recent advances in 4D topology.

Findings

Established concordances between standard and homologous surfaces in $S^2\times S^2$

Unified recent theorems and constructions to achieve new concordance results

Enhanced understanding of surface relations in 4-manifolds

Abstract

In this note, we combine the recent 4-dimensional light bulb theorem of David Gabai and a recent construction of concordances for knots in $S^2\times S^1$ due to Eylem Zeliha Yildiz to construct a concordance between the standard surface of genus $g$ in $S^2\times S^2$ and any homologous surface.