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Direct and indirect constructions of locally flat surfaces in 4-manifolds

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Ray,  Arunima
Max Planck Institute for Mathematics, Max Planck Society;

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2412.18423.pdf
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Ray, A. (submitted). Direct and indirect constructions of locally flat surfaces in 4-manifolds.


Cite as: https://hdl.handle.net/21.11116/0000-0010-5F66-2
Abstract
There are two main approaches to building locally flat embedded surfaces in 4-manifolds: direct methods which geometrically manipulate a given map of a surface, and more indirect methods using surgery theory. Both methods rely on Freedman--Quinn's disc embedding theorem. These are the lecture notes for a minicourse giving an introduction to both methods, by sketching the proofs of the following results: every primitive second homology class in a closed, simply connected 4-manifold is represented by a locally flat torus (Lee--Wilczyński); and every Alexander polynomial one knot in S3 is topologically slice (Freedman--Quinn).