## the generalized Poincaré conjecture?

Who?
Ekin Ergen (TU Berlin)
When?
2022/07/15, 13:00
Before the MATH+ Friday Colloquium by Prof. Arunima Ray (abstract, video recording)
Where?
TU Berlin, Hardenbergstraße 36 (directions)
Eugene-Paul-Wigner-Gebäude (EW), Lecture hall EW 201
In addition, the talked is live-streamed online (via zoom). The link has been sent out via the usual mailing lists; please contact the organisers if you have not received the email and would like to join the livestream.
We are going to explore a higher-dimension version of the Poincaré conjecture. In dimension three, this corresponds to the only Millennium Prize problem that is solved as of today. Roughly, the conjecture tells us that, if a manifold is homotopy equivalent to a sphere of its dimension, it is a sphere. We are going to discuss the history of this conjecture, and sketch a proof of the higher-dimension version via the $h$-cobordism theorem, due to Smale (1960). We are also going to introduce handle decompositions and the so-called Whitney trick, due to Whitney, which helps us tidy up handles. Prepare to see a lot of great achievements and of course, a lot of pictures!