Where do holes come from? (David Brown)

The Image Computing Spectral Sequence

16:00, October 18, Kennedy Seminar Room 2

Abstract: Consider the (abstract) Klein Bottle – this has two one dimensional holes in it – one normal hole and one “weird” one. The commonly known picture of the Klein Bottle with a self-intersection circle also has two one dimensional holes in it, so all seems well. However, the map that maps one to the other actually “kills” the “weird” hole in some sense – thus it is a mystery where the new hole has come from. In this talk, we will explore this idea of “holes” not coming from the domain of a map, in fact they come from the multiple point spaces. We will look at a wonderful piece of machinery called the Image Computing Spectral Sequence, though I will try to put emphasis on pictures rather than the full details of what is going on, and show that in fact most cases have a strong link between holes in the image and holes in the multiple point spaces.