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      Brunnian exotic surfaces links in the 4-ball

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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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          Author and article information

          Journal
          25 June 2021
          Article
          2106.13776
          7a8154d5-1e90-4b2d-afef-f9c90c208d7e

          http://creativecommons.org/licenses/by/4.0/

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          Custom metadata
          57K40, 57K45 (Primary) 57N35 (Secondary)
          37 pages, 36 figures, 2 appendices, 1 footnote, 1 stanza
          math.GT

          Geometry & Topology
          Geometry & Topology

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