An infinite family of links with critical bridge spheres

Publication Year:
2017
Usage 93
Downloads 60
Abstract Views 33
Repository URL:
http://ir.uiowa.edu/etd/5615; https://ir.uiowa.edu/cgi/viewcontent.cgi?article=7095&context=etd
Author(s):
Rodman, Daniel
Publisher(s):
University of Iowa
Tags:
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.