Oberseminar "Mathematische Logik" - Matthias Uschold

Many topological invariants admit restrictions in terms of their computability. For example, given two manifolds of the same dimension, we can define the set of mapping degrees between them. (I'll give a gentle introduction in my talk  to this set of integers.) We will prove that these sets are recursively enumerable, placing an important restriction on which sets can occur as such mapping degree sets. Similar phenomena are ubiquitous in topology: time permitting, I'll state some computability results on other invariants. I'll try to make this talk accessible without prior knowledge in topology (apart from the definition of a (smooth) manifold and continuous maps between them).