Seminar Event Detail


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 first-order way, i.e., without reference to curves or homeomorphisms or other higher-order objects.


Speaker:  Matthew Harrison-Trainor
Institution:  UM

Event Organizer:   Andreas R Blass


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