Rational homotopy theory

Summary

Rational homotopy theory studies spaces up to maps that induce isomorphisms on rational homotopy groups, so it ignores all torsion. For simply connected spaces this coarser theory is completely algebraic. By the work of Quillen and Sullivan, rational homotopy types correspond to commutative differential graded algebras over $\Q$, or to differential graded Lie algebras. Concrete invariants such as Sullivan minimal models make many questions computable that are out of reach integrally.