Searching for slice alternating knots.

Brendan Owens (Glasgow)

Monday 23rd October, 2017 16:00-17:00 Maths 311B


Slice knots go back to a paper of E. Artin in the 1920s; they are cross-sections of knotted 2-spheres in the 4-sphere.  They can be used in the construction of exotic smooth structures on R^4 and are in some sense the tip of the iceberg of strangeness that is 4-dimensional topology.  I will report on a joint project with Frank Swenton whose goal is to develop an algorithm to determine whether an alternating knot is slice.  We can’t do this yet but we have an algorithm that has been remarkably, and indeed mysteriously, successful in finding a great deal of new slice knots.

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