Aspherical space
In topology, a branch of mathematics, an aspherical space is a topological space with all homotopy groups πn(X) equal to 0 when n>1.
If one works with CW complexes, one can reformulate this condition: an aspherical CW complex is a CW complex whose universal cover is contractible. Indeed, contractibility of a universal cover is the same, by Whitehead's theorem, as asphericality of it. And it is an application of the exact sequence of a fibration that higher homotopy groups of a space and its universal cover are same. (By the same argument, if E is a path-connected space and p: E → B is any covering map, then E is aspherical if and only if B is aspherical.)