In 1963 Milnor proposed a list of seven problems that he considered the toughest and most important in geometric topology at the time. The first among these was the double suspension problem: given a non-simply connected 3-manifold with the homology of the 3-sphere, is the double suspension homeomorphic to the 5-sphere? Notably the first suspension is not even a manifold. In 1979 Cannon proved the double suspension theorem using tools from decomposition space theory. The minicourse will introduce the latter field, whose other successes include the Schoenflies theorem in all dimensions and Freedman's proof of the Poincare conjecture in dimension four; as well as indicate, in broad strokes, Cannon's proof of the double suspension theorem. Along the way we will meet various notions of generalised manifolds, and possibly curious examples thereof.

Meeting ID: 932 6354 3312

For passcode contact Christian Kaiser (kaiser@mpim-bonn.mpg.de)

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