Flat grafting deformations of quadratic differentials on surfaces.

In this paper we introduce flat grafting as a deformation of quadratic differentials on a surface of finite type that is analogous to the grafting map on hyperbolic surfaces. Flat grafting maps are generic in the strata structure and preserve parallel measured foliations. The 1-parameter family obtained by flat grafting allows us to explicitly describe a path connecting any pair of quadratic differentials. The slices of quadratic differentials closed under flat grafting maps with a fixed direction arise naturally and we prove rigidity properties with respect to the lengths of closed curves. [ABSTRACT FROM AUTHOR]