Surface representatives of second homology classes can be used to give geometric invariants for second homology classes, the most prominent examples are the genus and the Euler characteristic. In this talk I will introduce the minimal genus problem, explain why determining the minimal genus of a given homology class is in general undecidable, and how to compute it for a large class of "negatively-curved" spaces including 2-dimensional CAT(-1)-complexes. This will need a normal form result proven by me and Mark Pedron, that extends a theorem by Edmonds on maps between surfaces.
Zoom meeting ID: 919-9946-8404
Password: see email announcement or contact the seminar organisers:
Tobias Barthel (barthel.tobi[at]gmail.com)
David Gay (dgay[at]uga.edu)
Arunima Ray (aruray[at]mpim-bonn.mpg.de)
Links:
[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] http://www.mpim-bonn.mpg.de/TopologySeminar