Serre spectral sequence information

the Serre spectral sequence (sometimes Leray–Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an...

algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization...

In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. It is usually seen nowadays...

_{i-1}(S^{7}).} Spectral sequences are important tools in algebraic topology for computing (co-)homology groups. The Leray-Serre spectral sequence connects the...

is a general source of spectral sequences. It is common especially in algebraic topology; for example, Serre spectral sequence can be constructed by first...

It was introduced by Gysin (1942), and is generalized by the Serre spectral sequence. Consider a fiber-oriented sphere bundle with total space E, base...

In mathematics, the Adams spectral sequence is a spectral sequence introduced by J. Frank Adams (1958) which computes the stable homotopy groups of topological...

techniques than the definitions might suggest. In particular the Serre spectral sequence was constructed for just this purpose. Certain homotopy groups...

Most modern computations use spectral sequences, a technique first applied to homotopy groups of spheres by Jean-Pierre Serre. Several important patterns...

Serre fibration K ( N , 1 ) → K ( G , 1 ) → K ( H , 1 ) {\displaystyle K(N,1)\to K(G,1)\to K(H,1)} which can be put through a Serre spectral sequence...

plays an important role in homotopy theory under the name of the Serre spectral sequence. In that case, the higher direct image sheaves are locally constant...

rational homotopy theory, the Halperin conjecture concerns the Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician...

theorem, Craig–Lyndon interpolation and the Lyndon–Hochschild–Serre spectral sequence. Lyndon was born on December 18, 1917, in Calais, Maine, the son...

algebra Homological algebra K-theory Lie algebroid Lie groupoid Serre spectral sequence Sheaf Topological quantum field theory Fraleigh (1976, p. 163)...

and covering spaces as special cases, and can be proven by the Serre spectral sequence on homology of a fibration. For fiber bundles, this can also be...

colleague there was Hugh Dowker, who in 1951 drew his attention to the Serre spectral sequence. In 1952, Hilton moved to DPMMS in Cambridge, England, where he...

calculation in stable homotopy theory (which can be done with the Serre spectral sequence, Freudenthal suspension theorem, and the Postnikov tower). The...

Jean-Pierre Serre of some homotopy groups of spheres, using the compatibility of transgressive differentials in the Serre spectral sequence with the Steenrod...

Henri Cartan and Jean-Pierre Serre, he reformulated and strengthened their method of killing homotopy groups in spectral sequence terms, creating the basic...

Lyndon-Hochschild-Serre spectral sequence, Bull. Amer. Math. Soc., Vol. 79, 1973, pp. 796–799 doi:10.1090/S0002-9904-1973-13321-X (See Lyndon–Hochschild–Serre spectral...

{\displaystyle H^{*}(G)} is that arising from the edge maps in the Serre spectral sequence of the universal bundle G → E G → B G {\displaystyle G\to EG\to...

P_{E}\to M} hence the Serre spectral sequence can be applied. From general theory of spectral sequences, there is an exact sequence 0 → E 3 0 , 1 → E 2...

multiplication action of H on G, and we can use the cohomological Serre spectral sequence of this bundle to understand the fiber-restriction homomorphism...