Time: 

15:10–17:00, November 3 (Tue) and 5 (Thu), 2026; 

15:10–17:00, November 10 (Tue) and 12 (Thu), 2026

Abstract:

The four two-hour lectures will focus mainly on deformations of Haken manifolds, including a version of Johannson's Deformation Theorem. Dehn's Lemma, the Loop Theorem and their generalisation by Waldhausen to a version of the Annulus Theorem will be assumed. Later on, we will assume Scott's Relative Annulus Theorem. We will start with an easy proof of Waldhausen's Homeomorphism Theorem, based on the Gadgil–Swarup paper on the arXiv, and then a special case of Johannson's Deformation Theorem. The first part of the (somewhat informal) talks will be based on three papers: partly on Neumann–Swarup, partly on Scott–Swarup (Transactions of the AMS, 2001) and partly on the Reeves–Scott–Swarup paper on deformations of Poincaré duality pairs. We will then move on to questions about, and generalisations of, the results described above. These will include new proofs of some of the earlier results, as well as generalisations and open problems, and will be suitable for beginning graduate students.