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Do homology 3-spheres bound homology 4-balls?

Sohaib Khalid
Schedule: 
Friday, April 16, 2021 - 11:00 to 12:00
Location: 
Online
Location: 
Zoom
Abstract: 

Whether a given homology 3-sphere bounds a homology 4-ball is a subtle issue. It is an astonishing fact that its solution depends on whether we require the bounding manifold to be smoothable or not! In the not-necessarily-smoothable case, this can always be done by a ground-breaking result of Freedman. In the smoothable case, there are various known obstructions. In this talk, we will study these matters and describe one such obstruction arising from the study of spin structures on closed 4-manifolds called the Rokhlin invariant.

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