An official website of the United States government
Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to non-federal websites. Their policies may differ from this site.
-
Abstract We show that there exist split, orientable, 2‐component surface‐links in with non‐isotopic splitting spheres in their complements. In particular, for non‐negative integers with , the unlink consisting of one component of genus and one component of genus contains in its complement two smooth splitting spheres that are not topologically isotopic in . This contrasts with link theory in the classical dimension, as any two splitting spheres in the complement of a 2‐component split link are isotopic in .more » « less
-
For every integerg\ge 2we construct 3-dimensional genus-g1-handlebodies smoothly embedded inS^{4}with the same boundary, and which are defined by the same cut systems of their boundary, yet which are not isotopic rel. boundary via any locally flat isotopy even when their interiors are pushed intoB^{5}. This proves a conjecture of Budney–Gabai for genus at least 2.more » « less
-
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.more » « less
