Date: Thursday, February 24, 2022
Location: 2866 East Hall (4:00 PM to 5:30 PM)
Title: Finding an atlas for a closed surface
Abstract: A topological manifold is a topological space for which there exists an atlas but, unlike smooth manifolds, the atlas is not part of the structure of the manifold. Given a topological manifold, how hard is it to recover an atlas? We consider this question for closed surfaces and prove that every computable Polish space homeomorphic to a closed surface admits an arithmetic atlas, and indeed an arithmetic triangulation. This is as simple as one could reasonably hope for; essentially, the locally Euclidean structure of a surface can be recovered from the topological structure in a firstorder way, i.e., without reference to curves or homeomorphisms or other higherorder objects.
Files:
Speaker: Matthew HarrisonTrainor
Institution: UM
Event Organizer: Andreas R Blass ablass@umich.edu
