Dyer-Lashof operations in 𝐾-theory

Abstract

operations were first introduced by Araki and Kudo in These operations were later used by Dyer and Lashof to determine H*(QY;Z P ) as a functor of H*(Y;Z P ) This has had many important applications. Hodgkin and Snaith independently defined a single secondary operation in if-homology (for p odd and p = 2 respectively) which was analogous to the sequence of Dyer-Lashof operations in ordinary homology In this note we describe new primary Dyer-Lashof operations in if-theory which completely determine K*(QY;Z P ) in general.