Finite covers of surfaces and simple closed curves
Justin Malestein (Oklokoma)
Monday 19th November, 2018 15:00-16:00 Maths 311B
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 consequence 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.