Localization genus of classifying spaces

Abstract

We show that for a large class of torsionfree classifying spaces, K-theory filtered ring is an invariant of the genus. We apply this result in two ways. First, we use it to show that the powerseries ring on n indeterminates over the integers admits uncountably many mutually non-isomorphic [lambda]-ring structures. Second, we use it to study the genus of infinite quaternionic projective space. In particular, we describe spaces in the genus of infinite quaternionic projective space which occur as targets of essential maps from infinite complex projective space, and we compute explicitly the homotopy classes of maps in these cases.