Interactions between topology and geometry in low dimensions

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This PhD project will delve into the area of low dimensional topology. In the realm of 3-manifolds the topological and the geometric structures inform each other. These interactions are less strong in dimension 4, but gain prominence when studying 3-manifolds as boundaries of 4-manifolds. The student will explore the connections between topology and contact and symplectic geometry using tools such as handle decompositions, Kirby calculus, Dehn surgeries and Lefschetz fibrations.