| Résume | Several notions of computability can be defined for compact subsets of Euclidean spaces. Some of them turn out to be equivalent for certain sets - we then say that the set has ``computable type''. Miller (2002) proved that n-dimensional spheres have computable type, and Iljazovic (2013) proved that closed manifolds have computable type. We study the case of finite simplicial complexes and obtain several topological characterizations of the complexes having computable type. We also relate the notion of computable type to the descriptive complexity of topological invariants, and investigate the expressiveness of low complexity invariants. This work was done in collaboration with Djamel Eddine Amir. |
