On formal group laws over the quotients of Lazard’s ring

We present a formal power series {\sum A_{ij}x^{i}y^{j}} over the Lazard ring Λ and the formal group laws {F_{n}} , {n\geq 2} , over the quotient rings of Λ. For each {F_{n}} , we construct a complex cobordism theory with singularities with the coefficient ring {\mathbb{Q}[p_{1},\dots,p_{2n}]} , with parameters {p_{i}} , {|p_{i}|=2i} .

Central Cohomology Operations and K-Theory

For stable degree 0 operations, and also for additive unstable operations of bidegree (0, 0), it is known that the centre of the ring of operations for complex cobordism is isomorphic to the corresponding ring of connective complex K-theory operations. Similarly, the centre of the ring of BP operations is the corresponding ring for the Adams summand of p-local connective complex K-theory. Here we show that, in the additive unstable context, this result holds with BP replaced by BP〈n⌰ for any n. Thus, for all chromatic heights, the only central operations are those coming from K-theory.