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 directly one uses some slightly weaker theories derived from it, such as Brown–Peterson cohomology or Morava K-theory, that are easier to compute.
The generalized homology and cohomology complex cobordism theories were introduced by Atiyah (1961) using the Thom spectrum.
... The coproduct is given by where the notation 2i means take the piece of degree 2i ... This can be interpreted as follows ...
... and is naturally isomorphic to Lazard's universal ring, and is the cobordism ring of stably almost complex manifolds ...
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