Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials
Anton Zorich - IRMAR, Université Rennes 1, Campus de Beaulieu, 35042 Rennes cedex, France (email) Abstract:
Moduli spaces of Abelian and quadratic differentials are stratiﬁed
by multiplicities of zeroes; connected components of the strata correspond
to ergodic components of the Teichmüller geodesic ﬂow. It is known that the
strata are not necessarily connected; the connected components were recently
classiﬁed by M. Kontsevich and the author and by E. Lanneau. The strata can
be also viewed as families of ﬂat metrics with conical singularities and with
$\mathbb Z$/$2 \mathbb Z$-holonomy.
Keywords: Teichmüller geodesic flow, moduli space of
quadratic differentials, Jenkins-Strebel differential, spin
structure, interval-exchange transformation, Rauzy class.
Received: October 2007; Revised: November 2007; Available Online: November 2007. |