Brunnian exotic surface links in the 4-ball

Kyle Hayden; Alexandra Kjuchukova; Siddhi Krishna; Maggie Miller; Mark Powell; Nathan Sunukjian

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arXiv · 2106.13776

Brunnian exotic surface links in the 4-ball

Kyle Hayden·Alexandra Kjuchukova·Siddhi Krishna·Maggie Miller·Mark Powell·Nathan Sunukjian

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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.

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BibTeX RIS

Kyle Hayden, Alexandra Kjuchukova, Siddhi Krishna, Maggie Miller, Mark Powell, Nathan Sunukjian. 2021-06-25. Brunnian exotic surface links in the 4-ball. https://arxiv.org/abs/2106.13776

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