Vortrag: "How to draw up to five-dimensional manifolds"
Hansjörg Geiges (Köln)
- https://www.uni-giessen.de/de/fbz/fb07/fachgebiete/mathematik/mathematik/kalender/2015/2015-11-05
- Vortrag: "How to draw up to five-dimensional manifolds"
- 2015-11-05T17:00:00+01:00
- 2015-11-05T18:00:00+01:00
- Hansjörg Geiges (Köln)
05.11.2015 von 17:00 bis 18:00 (Europe/Berlin / UTC100)
Hörsaal des Mathematischen Instituts in der Arndtstraße 2, 1. Stock, Raum 111
Ein Vortrag im Rahmen des Mathematischen Kolloquiums und des Seminars "Gruppen, Geometrie, Dynamik".
Um 16:30 Uhr gibt es vorab Tee und Kekse im Runden Zimmer der Bibliothek des Mathematischen Instituts.
Die Dozenten des Mathematischen Instituts laden alle Interessierten herzlich ein.
Abstract
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 draw 1-dimensional pictures truly representing the topology of surfaces. By analogy, one can draw 2-dimensional pictures of 3-manifolds (Heegaard diagrams), and 3-dimensional pictures of 4-manifolds (Kirby diagrams).
With a little trick, one can even draw 2-dimensional (sic!) pictures of at least some 5-manifolds.
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.