Good spaces and Complexity.

Fixing a space A, the class of spaces C(A) is the collection of spaces which can be built out of A by using weak equivalences and homotopy colimits. The A complexity of a space X measures how difficult it is to built X from A with these operations. In this talk we will discuss some formulae for A-complexity, a special collection of spaces A called good, and A-complexity of spaces when A is good.