Finite covers of surfaces and simple closed curves

In this talk, I will present examples of finite covers of punctured surfaces where the first rational homology
is not spanned by lifts of simple closed curves. Additionally, I will discuss analogous results for primitive
elements and the homology of finite index subgroups of a free group. I will also present a couple consequences
of these results including a theorem that Out(F_n) modulo the group generated by kth powers of transvections
often has infinite order elements. This is joint work with Andrew Putman.