Tor decomposition of bup* (BZ/p)^n

Abstract

We decompose bup* (BZ/p)^n, the connective unitary K- theory with p-adic coefficients of the n-fold smash product of the classifying space for the cyclic group of prime order p, as a direct sum of some graded groups, which include the graded groups bup* (BZ/p) and Tor^1_{\Z_p[v]}(bu_{p^*}(B\Z/p), bu_{p^*}(B\Z/p))[-1]. We deal with the results in [Theorem 3.8]{MK17} together with the Kunneth sequence for bu_{p^*}(B\Z/p)^n, to explain that there is no extension problem for this Kunneth sequence, for any finite number n not just for n=2 and therefore the middle term of this sequence is a direct sum of the left and the right side.