In mathematics, the Landweber exact functor theorem, named after
Peter Landweber
Peter Steven Landweber (born August 17, 1940, in Washington D. C.) is an American mathematician working in algebraic topology.
Landweber studied at the University of Iowa (B.SC. 1960) and the Harvard University (master's degree 1961), where he gra ...
, is a theorem in
algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism, though usually most classify ...
. It is known that a
complex orientation of a
homology theory leads to a
formal group law In mathematics, a formal group law is (roughly speaking) a formal power series behaving as if it were the product of a Lie group. They were introduced by . The term formal group sometimes means the same as formal group law, and sometimes means one o ...
. 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.
Statement
The coefficient ring of
complex cobordism In mathematics, complex cobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally powerful cohomology theory, but can be quite hard to compute, so often instead of using it ...
is