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Knot concordance and slice movies

Brendan Owens blackboardThis board belongs to University of Glasgow researcher Brendan Owens. The pictures on the right show a ‘slice movie’ which is used to prove that two knots are concordant to each other. The pictures are essentially 3D slices through a 4D disc; the ‘singularity’ where two parts of the knot appear to intersect is an illusion caused by the particular projection.  The long exact sequences on the left are the technical algebraic topology used to explore the crazy world of 4-dimensional knot theory, where geometrical intuition so frequently fails.

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