有理同伦论

　　R，ational homotopy theory has the disadvantage of discarding a
considerable amount of information.  For example， the homotopy
groups of the sphere S’2 are non-zero in infinitelv many degrees
whereas its rational homotopy groups vanish in all degrees above 3.
By contrast， rational homotopy theory has the advantage of being
remarkably computational. For example， there is not even a
conjectural de*ion of all the homotopy groups of any simply
connect.ed finite CW complex， whereas for many of these the
rational groups can be explicitly determined.  And while
rational homotopy theory is indeed simpler than ordinary homotopy
theory， it is exactly this simplicity that makes it possible to
address （if not alway-s to solve） a number of fundamental
questions.