Topological index and square plat projections (Puttipong Pongtanapaisan)

The bridge distance and the topological index are measures of the complexity of the bridge splitting of a knot. In 2016, Johnson and Moriah gave a formula for the bridge distance of the canonical bridge sphere of a knot in a highly twisted plat projection in terms of the height and the width of the plat. Essentially, if the plat is high, then the bridge distance is high and the topological index equals one. Not much is known about the topological index of the bridge sphere when the plat is not high. In this talk, I will show that if the plat is square, then the topological index equals two. This is joint work with Daniel Rodman.