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Spectral sequence information


In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization of exact sequences, and since their introduction by Jean Leray (1946a, 1946b), they have become important computational tools, particularly in algebraic topology, algebraic geometry and homological algebra.

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Spectral sequence

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

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Leray spectral sequence

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

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Serre spectral sequence

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

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Stellar classification

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demonstrated that the O-B-A-F-G-K-M spectral sequence is actually a sequence in temperature. Because the classification sequence predates our understanding that...

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Adams spectral sequence

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

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Grothendieck spectral sequence

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algebra, the Grothendieck spectral sequence, introduced by Alexander Grothendieck in his Tôhoku paper, is a spectral sequence that computes the derived...

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Chromatic spectral sequence

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chromatic spectral sequence is a spectral sequence, introduced by Ravenel (1978), used for calculating the initial term of the Adams spectral sequence for Brown–Peterson...

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Homological algebra

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topological spaces, and other "tangible" mathematical objects. A spectral sequence is a powerful tool for this. It has played an enormous role in algebraic...

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Bockstein spectral sequence

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In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod p coefficients and the homology reduced mod p. It...

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May spectral sequence

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spectral sequence is a spectral sequence, introduced by J. Peter May (1965, 1966). It is used for calculating the initial term of the Adams spectral sequence...

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Sequence

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sequence of vector spaces and linear maps, or of modules and module homomorphisms. In homological algebra and algebraic topology, a spectral sequence...

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Quillen spectral sequence

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mathematics known as K-theory, the Quillen spectral sequence, also called the Brown–Gersten–Quillen or BGQ spectral sequence (named after Kenneth Brown, Stephen...

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Fibration

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

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Universal coefficient theorem

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coefficient ring A is Z/pZ, this is a special case of the Bockstein spectral sequence. Let G be a module over a principal ideal domain R (e.g., Z or a field...

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EHP spectral sequence

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In mathematics, the EHP spectral sequence is a spectral sequence used for inductively calculating the homotopy groups of spheres localized at some prime...

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Red dwarf

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earlier stars. The most recent surveys place the coolest true main-sequence stars into spectral types L2 or L3. At the same time, many objects cooler than about...

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Exact couple

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

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Frank Adams

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thesis, written under the direction of Shaun Wylie, was titled On spectral sequences and self-obstruction invariants. He held the Fielden Chair at the...

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Sheaf cohomology

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Grothendieck's 1957 Tôhoku paper. Sheaves, sheaf cohomology, and spectral sequences were introduced by Jean Leray at the prisoner-of-war camp Oflag XVII-A...

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Hyperhomology

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a variety X over a field k, the second spectral sequence from above gives the Hodge-de Rham spectral sequence for algebraic de Rham cohomology: E 1 p...

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