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Peter Kronheimer: Genus versus double-points for immersed surfaces (RLGTS, 5 May 2020)

Lukas Lewark
Peter Kronheimer: Genus versus double-points for immersed surfaces (RLGTS, 5 May 2020)

Abstract:

If X is a simply-connected closed 4-manifold containing an oriented embedded surface S of genus g, is there always an immersed sphere S' which represents the same homology class and has only g transverse double-points? Colloquially, can we "trade handles for double points"? This is an open question, though a "relative" version of the question (concerning surfaces in the 4-ball bounding a given knot in the 3-sphere) is known to have a negative answer. For closed surfaces in closed 4-manifolds, a particularly interesting class of examples comes from algebraic geometry, and includes the question of whether two smooth quintic surfaces can intersect in a singular rational curve. We will explore whether gauge theory might be a tool that can be used to explore these questions.

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Erstellt am: 07.05.2020 12:25
Letzte Aktualisierung: 07.05.2020 12:30