A splitting theorem for connected moravaK-theories

Abstract

LetX be a connected, locally finite spectrum and letk(n) (n>-1) denote the (−1)-connected cover of then-th MoravaK-Theory associated to the primep.k(n) is aBP-module spectrum with π_*(k(n)) ≅ ℤ _p [υ _n ] where |v _n | = 2(p ⁿ-1). We prove the following splitting theorem: Thek(n) ^*-torsion ofk(n) ^* (X) is already annihilated byv ^e_n (e≥1) if and only ifk(n)ΛX is homotopy equivalent to a wedge of spectrak(n) and^r k(n) (0≤r≤e-1) where^r k(n) denotes ther-th Postnikov factor ofk(n). Moreover we investigate splitting conditions for^r k(n)ΛX.