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 Michael Atiyah (1961) using the Thom spectrum.
In mathematics, complexcobordism is a generalized cohomology theory related to cobordism of manifolds. Its spectrum is denoted by MU. It is an exceptionally...
unoriented cobordism. Other cobordism theories do not reduce to ordinary homology in this way, notably framed cobordism, oriented cobordism and complex cobordism...
derived. Cobordism studies manifolds, where a manifold is regarded as "trivial" if it is the boundary of another compact manifold. The cobordism classes...
In mathematics, the oriented cobordism ring is a ring where elements are oriented cobordism classes of manifolds, the multiplication is given by the Cartesian...
different flavors of cobordism groups, based on studying a space by considering all maps from it to manifolds: unoriented cobordism M O ∗ ( X ) {\displaystyle...
In mathematics, algebraic cobordism is an analogue of complexcobordism for smooth quasi-projective schemes over a field. It was introduced by Marc Levine...
element of non-zero degree is nilpotent; the nilpotence theorem on complexcobordism implies Nishida's theorem.[citation needed] Example: If η is the generator...
This result extends to other cohomology theories as well, such as complexcobordism and is instrumental in computing its cohomology ring Ω U ∗ ( { p t...
complexcobordism. Further, Milnor and C. T. C. Wall used the spectral sequence to prove Thom's conjecture on the structure of the oriented cobordism...
on cohomology of groups and algebraic K-theory. He also worked on complexcobordism, showing that its formal group law is essentially the universal one...
a fuzzy set The standard measure function name in measure theory Complexcobordism, an extraordinary cohomology theory Micro-, SI (metric, "μ-") prefix...
work was in cobordism theory. He calculated the differential in the Atiyah-Hirzebruch spectral sequence in K-theory and complexcobordism theory, constructed...
ring spectra include singular homology with coefficients in a ring, complexcobordism, K-theory, and Morava K-theory. Highly structured ring spectrum Adams...
(m,k)-handlebody of genus g . A handle presentation of a cobordism consists of a cobordism W where ∂ W = M 0 ∪ M 1 {\displaystyle \partial W=M_{0}\cup...
are studied in a variety of contexts in algebraic topology, such as complexcobordism theory, and the other oriented cohomology theories. Denote the i {\displaystyle...
homotopy theory leading to the Ravenel conjectures. In this picture, complexcobordism and Morava K-theory control many qualitative phenomena, which were...
cohomology theories called bordism and cobordism, and pointed out that many of the deep results on cobordism of manifolds found by René Thom, C. T. C...
encodes the same information as the cobordism class [ M ] {\displaystyle [M]} . This can be shown by using a cobordism W {\displaystyle W} and finding an...
2(i + j − 1)). Daniel Quillen proved that the coefficient ring of complexcobordism is naturally isomorphic as a graded ring to Lazard's universal ring...
manifold. For context see timeline of manifolds. Jean Dieudonné wrote that cobordism returns to the attempt in 1895 to define homology theory using only (smooth)...
1016/0021-8693(66)90009-3, MR 0193126 Ravenel, Douglas C. (2003), Complexcobordism and stable homotopy groups of spheres (2nd ed.), AMS Chelsea, ISBN 978-0-8218-2967-7...
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