Tautological rings of stable map spaces
  We find a set of generators and relations for the system of extended tautological rings associated to the moduli spaces of stable maps in genus zero, admitting a simple geometrical interpretation. In particular, when the target is $\PP^n$, these give a complete presentation for the cohomology and Chow rings in the cases with/without marked points. 
Anca M. Mustata, Andrei Mustata