Topology of nonarchimedean analytic spaces and relations to complex algebraic geometry

Abstract

This note surveys basic topological properties of nonarchimedean analytic spaces, in the sense of Berkovich, including the recent tameness results of Hrushovski and Loeser. We also discuss interactions between the topology of nonarchimedean analytic spaces and classical algebraic geometry.

30 pages, 5 figures. v3: Final version, to appear in Bull. Amer. Math. Soc