Universal Teichmüller space in geometry and physics
Osmo Pekonen
Abstract
Lipman Bers' universal Teichmüller space, classically denoted by T(1), plays a significant role in Teichmüller theory, because all the Teichmüller spaces T(G) of Fuchsian groups G can be embedded into it as complex submanifolds. Recently, T(1) has also become an object of intensive study in physics, because it is a promising geometric environment for a non-perturbative version of bosonic string theory. We provide a non-technical survey of what is currently known about the geometry of T(1) and what is conjectured about its physical meaning.
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