Abstract: When you first heard about the Klein Bottle you might have been confounded by the fact that there is no good depiction of it. Why can’t people just draw a proper picture of the thing? One that does not self intersect? It turns out that it is impossible to “draw the Klein Bottle“ in R ^3 without self intersections, and this is a math fun fact that people often throw around but that is rarely proven (even in lectures on topology). In this Colloquium I want to close this gap by providing an elementary self-contained proof that the Klein bottle (and many more objects) cannot be “drawn in 3-d space“ without self intersections.
Why does the Klein Bottle look so weird?
27.05.2024 15:00 - 16:00
Organiser:
Vienna School of Mathematics
Location:
TUForMath-Room at Freihaus TU Wien, Wiedner Hauptstraße 8-10, 1040 Wien