Brunnian exotic surface links in the 4-ball

TL;DR

This paper constructs and analyzes exotic Brunnian surface links in the 4-ball, extending classical knot theory tools to higher dimensions to reveal new phenomena in 4-dimensional topology.

Contribution

It introduces two constructions of exotic Brunnian surface links in the 4-ball and adapts 3D knot theory tools for 4D topology analysis.

Findings

Provided explicit constructions of exotic Brunnian surface links.

Extended satellite operations and Bing doubling to 4-dimensional links.

Varied the number of components and genera in the constructed links.

Abstract

This paper investigates the exotic phenomena exhibited by links of disconnected surfaces with boundary that are properly embedded in the 4-ball. Our main results provide two different constructions of exotic pairs of surface links that are Brunnian, meaning that all proper sublinks of the surface are trivial. We then modify these core constructions to vary the number of components in the exotic links, the genera of the components, and the number of components that must be removed before the surfaces become unlinked. Our arguments extend two tools from 3-dimensional knot theory into the 4-dimensional setting: satellite operations, especially Bing doubling, and covering links in branched covers.