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...

algebra and number theory, the Lyndon spectral sequence or Hochschild–Serre spectral sequence is a spectral sequence relating the group cohomology of a normal...

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

subcategory Serre functor Serre spectral sequence Lyndon–Hochschild–Serre spectral sequence Serre–Swan theorem Serre–Tate theorem Serre's theorem in group...

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...

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

Hirzebruch pointed out a generalization of their spectral sequence that also generalizes the Serre spectral sequence, and reduces to it in the case where E =...

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

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

n − 1. The sequence for general n may be deduced from the case n = 1 by dimension-shifting or from the Lyndon–Hochschild–Serre spectral sequence. Gille &...

algebra techniques. Serre's thesis concerned the Leray–Serre spectral sequence associated to a fibration. Together with Cartan, Serre established the technique...

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

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

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...

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

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...

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

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

cohomology arises as the five-term exact sequence associated to the Lyndon–Hochschild–Serre spectral sequence H p(G/N, H q(N, A)) ⇒ H p+q(G, A) where G...

in Mathematics, vol. 91. Kronholm, W. (2010). "The RO(G)-graded Serre spectral sequence". Homology, Homotopy and Applications, 12(1):75-92. Dieck, T. (1987)...

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

{\displaystyle N} is a manifold of dimensions n {\displaystyle n} . The Serre spectral sequence is compatible with the above algebraic structures for both the...

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...

{\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...

Leray spectral sequence. This was exploited by Jean-Pierre Serre while he studied the homotopy groups of spheres using the Postnikov system and spectral sequences...

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...

functoriality. For instance, there is in general no Hochschild-Serre spectral sequence relating H i ( X ét , Z ℓ ) {\displaystyle H^{i}(X_{\text{ét}}...

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