Computable type: an overview

Abstract: A compact metrizable space X has computable type if for every set that is homeomorphic to X, semicomputability is equivalent to computability. This notion was first studied by Joe Miller in 2002, who showed that finite-dimensional spheres all have computable type. It was then developed by Zvonko Iljazović and his co-authors, who showed among many other results that compact manifolds also enjoy this property. I will present recent results on the notion of computable type, obtained in collaboration with Djamel Eddine Amir during his PhD, such as: a simple characterization of 2-dimensional simplicial complexes having computabe type, a proof that this property is not preserved by taking binary products.

geometric topologylogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic