Teichmuller space
for genus parametrizes pairs
of a genus Riemann surface and a homeomorphism
to a fixed surface of genus , up to
isotopy of . This is equivalent to parametrizing Riemann
surfaces with a choice of normalized generators of
.
It is naturally an open subset of
, homeomorphic to
a ball. It admits an action of the mapping class group
with finite stabilizers and with quotient
.

Jeffrey Herschel Giansiracusa
2005-06-27