Trisections of smooth 4-manifolds

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2022-6

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Şen, Eren

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The aim of this thesis is to provide an exposition of the theory of trisections of smooth 4-manifolds which were introduced by David T. Gay and Robion Kirby in 2012. We survey the theory by highlighting its essential elements and try to provide insight by making analogies between trisections and Heegaard splittings. The thesis also discusses the classification of genus 1 trisections and describes algorithms for passing between a Kirby diagram and a trisection diagram of a manifold in detail. In addition, by presenting and using the algorithm introduced by N. Castro, D. T. Gay, and J. Pinzón-Caicedo, we produce a relative trisection for the Mazur manifold bounded by the Brieskorn sphere Σ(2, 5, 7).

Subject Keywords

trisection, handlebody, trisection diagram, Kirby diagram

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https://hdl.handle.net/11511/98103

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

E. Şen, “Trisections of smooth 4-manifolds,” M.S. - Master of Science, Middle East Technical University, 2022.