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Surgery without tears

Kirby topology 2012This photo is of the board of Rob Kirby, who recently visited the University of Edinburgh to give a series of talks on the topology of manifolds. It shows a version of the Thom-Pontrjagin construction for connecting two components of the pre-image (under the map g) of a point (0,0), but doing so in a neighbourhood of the blue arc connecting the two components.  The two components are in red, and as the homotopy progresses the red components are pushed towards each other until they meet at a point, like a saddle, and then become a cylinder joining the two components. This is basically surgery on a 0-sphere.

With thanks to Andrew Ranicki for taking the photo and providing the title for this post.


One response

  1. The videos of Rob’s Edinburgh lectures are linked on
    Check out Carmen Rovi’s introduction to the trisection lecture!

    December 5, 2012 at 10:00 am

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