Mathematics Colloquia and Seminars

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Morse functions have proved useful in solving a number of problems concerning 3-manifolds. In particular, there is a nice correspondence between Morse functions on 3-manifolds and Heegaard splittings. After describing what makes a function a Morse function, the talk will focus on techniques of comparing two Morse functions on the same manifold and deformations which turn one function into the other. This will bring us to the subject of singularity theory, a generalization of Morse theory, after which the talk will abrubtly stop.

No background in Morse theory, differential geometry or geometric topology will be assumed. However, if you don't know what an open neighborhood is, please look it up a few minutes before the talk.