On a family of unitary representations of mapping class groups

For a compact surface $S = S_{g,n}$ with $3g + n \geq 4$, we introduce family of unitary representations the mapping class group Mod($S$) based on space measured foliations. this representations, show that none them has almost invariant vectors. As one application, obtain an inequality concerning action Teichmuller $S$. Moreover, using same method plus recent results about weak equivalence, also give classification, up to for quasi-representations respect geometrical subgroups.