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.

Read more about Complex Cobordism: Spectrum of Complex Cobordism, Formal Group Laws, Brown–Peterson Cohomology, Conner–Floyd Classes, Cohomology Operations

### Other articles related to "complex cobordism, cobordism, complex":

**Complex Cobordism**

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... The coproduct is given by where the notation 2i means take the piece of degree 2i ... This can be interpreted as follows ...

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“In the case of all other sciences, arts, skills, and crafts, everyone is convinced that a *complex* and laborious programme of learning and practice is necessary for competence. Yet when it comes to philosophy, there seems to be a currently prevailing prejudice to the effect that, although not everyone who has eyes and fingers, and is given leather and last, is at once in a position to make shoes, everyone nevertheless immediately understands how to philosophize.”

—Georg Wilhelm Friedrich Hegel (1770–1831)