The Brown-Peterson \([2^ k]\)-series revisited
The \([2^k]\)-series in Brown-Peterson theory arises from the associated formal group law \(F(X,Y)\) and the inductive definitions, \([1] X=X=F(0,X) =F(X,0)\), \([2] X= F(X,X)\), \([2^k] X=[2]([2^{k-1}]X)\). One can write \([2^k]=\sum_{0\leq s}a_{k,s} X^{s+1}\), \(a_{k,s} \in BP_{2s}\). The coefficients \(a_{k,s}\) generate the relations in the Brown-Peterson homology of \(BZ/2^k\). This paper shows that each coefficient \(a_{k,s}\) has a distinguished shortest monomial which is determined by the dyadic expansion of \(s+1\).
scientific article; zbMATH DE number 933079