Knotted Surfaces in 4-manifolds and Distances Between Them

Oliver Singh (Durham University)

Monday 25th January 16:00-17:00 Online


I will discuss knotted surfaces, isotopy classes of embedded surfaces in a given 4-manifold, and will define two notions of distance between them. These distances are integer-valued and are defined topologically: one in terms of regular homotopy; another in terms of stabilisation, a form of embedded surgery. I will outline a proof of an inequality between these distances; the proof is constructive and draws upon ideas pioneered by Gabai in the proof of the 4-dimensional light bulb theorem.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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