Mathematics Commons^™

Bridge Trisections And Classical Knotted Surface Theory, Jason Joseph, Jeffrey Meier, Maggie Miller, Miller Zupan

Department of Mathematics: Faculty Publications

We seek to connect ideas in the theory of bridge trisections with other wellstudied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney–Massey theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of …