In mathematics, a secondary cohomology operation is a functorial correspondence between cohomology groups. More precisely, it is a natural transformation...

In mathematics, the cohomology operation concept became central to algebraic topology, particularly homotopy theory, from the 1950s onwards, in the shape...

Spanier–Whitehead dual of a secondary cohomology operation. Peterson, F. P.; Stein, N. (1960), "The dual of a secondary cohomology operation", Illinois Journal...

Henri Cartan (1955) to be the algebra of stable cohomology operations for mod p {\displaystyle p} cohomology. For a given prime number p {\displaystyle p}...

In algebraic topology, the Massey product is a cohomology operation of higher order introduced in (Massey 1958), which generalizes the cup product. The...

secondary cohomology operations. The Adams–Novikov spectral sequence is an analogue of the Adams spectral sequence using an extraordinary cohomology theory...

cohomology class that detects non-triviality of the tangent bundle of spheres: to prove further results, one must use secondary cohomology operations...

supervision of Norman Steenrod. His dissertation was titled Secondary cohomology operations induced by the diagonal mapping. He received a degree in philosophy...

Peterson, Franklin P.; Stein, Norman (1960), "The dual of a secondary cohomology operation", Illinois Journal of Mathematics, 4 (3): 397–404, doi:10.1215/ijm/1255456056...

Adams was very long and complicated, using secondary cohomology operations. Atiyah showed how primary operations in K-theory could be used to give a short...

categories, "six operations") Yoga of the Grothendieck–Riemann–Roch theorem K-theory relation with intersection theory Schemes Topoi Étale cohomology and l-adic...

Eliashberg, N. Mishachev (2002, ISBN 978-0-8218-3227-1) 49 Secondary Cohomology Operations, John R. Harper (2002, ISBN 978-0-8218-3270-7) 50 An Invitation...

List of Boolean algebra topics List of category theory topics List of cohomology theories List of commutative algebra topics List of homological algebra...

smoothness from calculus. Instead it is built using sheaf theory and sheaf cohomology. Abstract harmonic analysis A modern branch of harmonic analysis that...

dmlcz/144360. JSTOR 1970556. Chern, S.-S.; Simons, J. (April 1971). "Some Cohomology Classes in Principal Fiber Bundles and Their Application to Riemannian...

{\mathcal {O}}} , its cohomology is used to define the following "secondary objects": secondary functions are elements of the cohomology H ¯ ∙ ( O ) = H ∙...

planes remain unchanged. Hiller, Howard (1986). "Crystallography and cohomology of groups". The American Mathematical Monthly. 93 (10): 765–779. doi:10...

Grothendieck of scheme theory, which allows using topological methods, including cohomology theories in a purely algebraic context. Scheme theory allowed to solve...

Grothendieck's derived functor cohomology has replaced Čech cohomology for technical reasons, actual calculations, such as of the cohomology of projective space...

algebraic topology. Among his major contributions, he worked on cohomology operations and homology of the Eilenberg–MacLane spaces, he introduced the...

Postnikov tower, which makes it so powerful to study while computing cohomology, is the fact the spaces X n {\displaystyle X_{n}} are homotopic to a CW...

including general relativity, invariant theory, characteristic classes, cohomology theory, Morse theory, Fiber bundles, Sheaf theory, Cartan's theory of...

Toda brackets vanish. This parallels the theory of Massey products in cohomology. The direct sum π ∗ S = ⨁ k ≥ 0 π k S {\displaystyle \pi _{\ast }^{S}=\bigoplus...

1951), Hungarian-Swiss mathematician, proved Serre's conjecture on Galois cohomology of classical groups Jillian Beardwood (1934–2019), British mathematician...

analysis and probability. 1957 Norman Steenrod (Princeton University): Cohomology operations. 1959 Joseph L. Doob (University of Illinois, Urbana-Champaign):...