On Morse Deformation

The following animations were part of a talk given on November 16, 2012 at Bridgewater. We see first a deformation of a surface, where the color shows the curvature (given by the discriminant formula). Then a similar deformation of a torus, where the total curvature is zero by Gauss-Bonnet. Then the island theorem is illustrated: the sum of the indices on an island is 1 (mountain peaks and sinks count as 1, saddle points count as -1).

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