In unstable homotopy theory, on the other hand, we
know the
v
_{
0
}
-periodic informations algebraically as
rational homotopy theory
.
The
v
_{
1
}
-periodic homotopy groups
are studied by D. Davis and others, but we
don’t have a systematic treatment which can be
called
v
_{
1
}
-periodic homotopy theory. Compared to stable homotopy
theory, we are still in the era before Ravenel
published his conjectures.