Simple space

In algebraic topology, a branch of mathematics, a simple space is a connected topological space that has a homotopy type of a CW complex and whose fundamental group is abelian and acts trivially on the homotopy and homology of the universal covering space, though not all authors include the assumption on the homotopy type.

For example, any topological group is a simple space (provided it satisfies the condition on the homotopy type).

are simple since the only nontrivial homotopy group is in degree

This means the only non-simple spaces are

Every connected topological space

This topology-related article is a stub.