Mathematics Colloquia and Seminars

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We will show how to construct a bijection between loops of Morse functions up to certain moves, loops in the pants complex up to certain moves, and smooth, orientable, closed 4-manifolds up to diffeomorphism. These constructions factor through cut systems on a surface, so that the 4-manifolds can be entirely encoded as curves on a surface. This gives a natural generalization of trisections which we call multisections, and we will explore their diagrams.