Small covers of big surfaces

Alan McLeay (University of Strathclyde)

Monday 28th November, 2022 16:00-17:00 Maths 311B

Abstract

Covering spaces and surfaces are ubiquitous in topology, but there are still some fundamental questions whose answers are not widely known. In particular, one can ask; given two surfaces, when does one admit a finite-sheeted cover over the other.

If the surfaces are closed, this reduces to an exercise in Euler characteristics. A result of Massey provides the answer when the surfaces are finite-type with boundary. In joint work with Ty Ghaswala, we look at what can be said about the remaining (uncountably many) cases.

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