# Category: Spectral sequences

Čech-to-derived functor spectral sequence
In algebraic topology, a branch of mathematics, the Čech-to-derived functor spectral sequence is a spectral sequence that relates Čech cohomology of a sheaf and sheaf cohomology.
Bockstein spectral sequence
In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod p coefficients and the homology reduced mod p. It is named after Meyer Bockstein.
Zeeman's comparison theorem
In homological algebra, Zeeman's comparison theorem, introduced by Zeeman, gives conditions for a morphism of spectral sequences to be an isomorphism.
Spectral sequence
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 sequenc
Atiyah–Hirzebruch spectral sequence
In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and Friedrich Hirzebruch in the special case of topo
EHP spectral sequence
In mathematics, the EHP spectral sequence is a spectral sequence used for inductively calculating the homotopy groups of spheres localized at some prime p. It is described in more detail in , chapter
Eilenberg–Moore spectral sequence
In mathematics, in the field of algebraic topology, the Eilenberg–Moore spectral sequence addresses the calculation of the homology groups of a pullback over a fibration. The spectral sequence formula
Five-term exact sequence
In mathematics, five-term exact sequence or exact sequence of low-degree terms is a sequence of terms related to the first step of a spectral sequence. More precisely, let be a first quadrant spectral
Arnold's spectral sequence
In mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient computational tool for reducing a function to
Hodge–de Rham spectral sequence
In mathematics, the Hodge–de Rham spectral sequence (named in honor of W. V. D. Hodge and Georges de Rham) is an alternative term sometimes used to describe the Frölicher spectral sequence (named afte
Halperin conjecture
In rational homotopy theory, the Halperin conjecture concerns the Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician Stephen Halperin.
Leray spectral sequence
In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. It is usually seen nowadays as a special case of the Grothendieck spectra
Chromatic spectral sequence
In mathematics, the chromatic spectral sequence is a spectral sequence, introduced by , used for calculating the initial term of the Adams spectral sequence for Brown–Peterson cohomology, which is in
Exact couple
In mathematics, an exact couple, due to William S. Massey, is a general source of spectral sequences. It is common especially in algebraic topology; for example, Serre spectral sequence can be constru
Grothendieck spectral sequence
In mathematics, in the field of homological algebra, the Grothendieck spectral sequence, introduced by Alexander Grothendieck in his Tôhoku paper, is a spectral sequence that computes the derived func
May spectral sequence
In mathematics, the May spectral sequence is a spectral sequence, introduced by J. Peter May . It is used for calculating the initial term of the Adams spectral sequence, which is in turn used for cal
Lyndon–Hochschild–Serre spectral sequence
In mathematics, especially in the fields of group cohomology, homological algebra and number theory, the Lyndon spectral sequence or Hochschild–Serre spectral sequence is a spectral sequence relating
Serre spectral sequence
In mathematics, the Serre spectral sequence (sometimes Leray–Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important tool in algebraic topolog