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Splitting spheres in $S^4$


Speaker: Maggie Miller, Stanford University
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Location: 2112 MSB
Start time: Thu, Jun 8 2023, 1:10PM

A 2-component link L is split if its components lie in disjoint balls. The boundary of either of these balls is called a splitting sphere for L. In the 3-sphere, 2-component split links have unique splitting spheres, meaning any two splitting spheres for L are isotopic in $S^3-L$. In this talk, we’ll discuss why this fails in dimension 4: many 2-component split links of surfaces in the 4-sphere do not have unique splitting spheres. (In fact, many unlinks have non-unique splitting spheres.) This is joint work with Mark Hughes and Seungwon Kim.