Mathematics – Geometric Topology
Scientific paper
2005-06-08
Mathematics
Geometric Topology
49 pages, 12 figures, submitted. major revision, typos corrected
Scientific paper
In two fundamental classical papers, Masur and Veech have independently proved that the Teichmueller geodesic flow acts ergodically on each connected component of each stratum of the moduli space of quadratic differentials. It is therefore interesting to have a classification of the ergodic components. Veech has proved that these strata are not necessarily connected. In a recent work, Kontsevich and Zorich have completely classified the components in the particular case where the quadratic differentials are given by the global square of Abelian differentials. Here we are interested in the complementary case. In a previous paper, we have described some particular component, namely the hyperelliptic connected components, and showed that some strata are non-connected. In this paper, we give the general classification theorem: up to four exceptional cases in low genera, the strata of meromorphic quadratic differentials are either connected, or have exactly two connected components. In this last case, one component is hyperelliptic, the other not. Our proof is based on a new approach of the so-called Jenkins-Strebel differential. We will present and use the notion of generalized permutations.
No associations
LandOfFree
Connected components of the strata of the moduli spaces of quadratic differentials does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Connected components of the strata of the moduli spaces of quadratic differentials, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Connected components of the strata of the moduli spaces of quadratic differentials will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-538706