Title: K(n+1) equivalence implies K(n) equivalence
Author: W. Stephen Wilson
Address: Johns Hopkins University, Baltimore, Maryland 21218
email: wsw@math.jhu.edu
abstract:
We give an entirely different proof of a recent result of
Bousfield's which states that if there is a map of spaces
inducing an isomorphism on the (n+1)st Morava K-theory then
it also induces an isomorphism on the n-th Morava K-theory.
The result relies heavily on the fundamentals introduced to
prove the results in Ravenel-Wilson-Yagita which in turn
relies on the forthcoming paper by Boardman-Wilson containing
a generalization of Quillen's theorem that MU^*(X) is
generated by non-negative degree elements when X is a finite
complex.