Surfaces in four-manifolds as viewed from curve complexes

Puttipong Pongtanapaisan (U. of Saskatchewan)


A knotted surface in a 4-manifold can be represented as a path in a graph whose vertices are pants decompositions. Understanding the lengths of these paths allows us to measure how complicated the knotted surface is. In this talk, we compute the minimum length of a path one needs to represent some surfaces from the knot table. This complexity measure is inspired by the work of Blair, Campisi, Taylor, and Tomova.

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