An infinite family of links with critical bridge spheres

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Rodman, Daniel
University of Iowa
Bridge sphere; Critical; Link; Plat position; Topologically minimal; Mathematics
thesis / dissertation description
A closed, orientable, splitting surface in an oriented 3-manifold is a topologically minimal surface of index n if its associated disk complex is (n-2)-connected but not (n-1)-connected. A critical surface is a topologically minimal surface of index 2. In this thesis, we use an equivalent combinatorial definition of critical surfaces to construct the first known critical bridge spheres for nontrivial links.