Complex cobordism is the generalized cohomology theory represented by the Thom spectrum 
of the universal complex vector bundles. Its coefficient
groups are bordism groups of closed manifolds whose stable tangent bundles carry
complex structures. The group operation is disjoint union and multiplication is Cartesian
product. A stably complex point represents the multiplicative
identity. The unit map from the sphere spectrum
to 
sends stable cohomotopy classes to complex-cobordism classes.
Complex Cobordism
See also
Bordism, CW-Complex, Smash Product, Sphere Spectrum, Topological Spectrum, Unitary ManifoldExplore with Wolfram|Alpha
References
Ravenel, D. C. Complex Cobordism and Stable Homotopy Groups of Spheres, 2nd ed. Providence, RI: Amer. Math. Soc., 2003. https://www.sas.rochester.edu/mth/sites/doug-ravenel/mybooks/ravenel.pdf.Cite this as:
Weisstein, Eric W. "Complex Cobordism." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ComplexCobordism.html