Teichmüller space via Kuranishi families

Arbarello, Enrico; Cornalba, Maurizio

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, pp. 89-116.

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

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