有理同伦论

　　R，ational homotopy theory has the disadvantage of discarding aconsiderable amount of information. For example， the homotopygroups of the sphere S'2 are non-zero in infinitelv many degreeswhereas its rational homotopy groups vanish in all degrees above 3.By contrast， rational homotopy theory has the advantage of beingremarkably computational. For example， there is not even aconjectural description of all the homotopy groups of any simplyconnect.ed finite CW complex， whereas for many of these therational groups can be explicitly determined. And whilerational homotopy theory is indeed simpler than ordinary homotopytheory， it is exactly this simplicity that makes it possible toaddress （if not alway-s to solve） a number of fundamentalquestions.