Landweber exact functor theorem

In mathematics, the Landweber exact functor theorem, named after Peter Landweber, is a theorem in algebraic topology. It is known that a complex orientation of a homology theory leads to a formal group law. The Landweber exact functor theorem (or LEFT for short) can be seen as a method to reverse this process: it constructs a homology theory out of a formal group law.

The coefficient ring of complex cobordism is ${\displaystyle MU_{*}(*)=MU_{*}\cong \mathbb {Z} [x_{1},x_{2},\dots ]}$, where the degree of ${\displaystyle x_{i}}$ is 2i. This is isomorphic to the graded Lazard ring ${\displaystyle {\mathcal {}}L_{*}}$. This means that giving a formal group law F (of degree −2) over a graded ring ${\displaystyle {\mathcal {}}R_{*}}$ is equivalent to giving a graded ring morphism ${\displaystyle L_{*}\to R_{*}}$. Multiplication by an integer n >0 is defined inductively as a power series, by

...
Wikipedia