Connected components of strata of quadratic differentials over Teichmuller space

Details Connected components of strata of quadratic differentials over Teichmuller space Connected components of strata of quadratic differentials over Teichmuller space

2008-05-04

arxiv.org/abs/0805.0434v1

Mathematics

Geometric Topology

14 pages, 3 figures

Scientific paper

In this paper, we study connected components of strata of the space of quadratic differentials lying over $\T_g$. We use certain general properties of sections of line bundles to put a upper bound on the number of connected components, and a generalized version of the Gauss map as an invariant to put a lower bound on the number of such components. For strata with sufficiently many zeroes of the same order we can state precisely the number of components.

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