We usually think of 2-dimensional manifolds as surfaces embedded in Euclidean 3-space. Since humans cannot visualise Euclidean spaces of higher dimensions, it appears to be impossible to give pictorial representations of higher-dimensional manifolds. However, one can in fact encode the topology of a surface in a 1-dimensional picture. By analogy, one can draw 2-dimensional pictures of 3-manifolds (Heegaard diagrams), and 3-dimensional pictures of 4-manifolds (Kirby diagrams). With the help of open books one can likewise represent at least some 5-manifolds by 3-dimensional diagrams, and contact geometry can be used to reduce these to drawings in the 2-plane. In this talk I shall explain how to draw such pictures and how to use them for answering topological and geometric questions. The work on 5-manifolds is joint with Fan Ding and Otto van Koert.
Donnerstag, den 18. Mai 2017 um 17.15 Uhr, in Mathematikon, INF 205, Hörsaal Mathematikon Donnerstag, den 18. Mai 2017 at 17.15, in Mathematikon, INF 205, Hörsaal Mathematikon
Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers