Teichmüller space via Kuranishi families

Abstract

In this partly expository note we construct Teichmiiller space by patching together Kuranishi families. We also discuss the basic properties of Teichmiiller space, and in particular show that our construction leads to simplifications in the proof of Teichmiiller's theorem asserting that the genus g Teichmiiller space is homeomorphic to a (6g-6)-dimensional ball.