Editing Spectral sequence (section)

== Further examples ==

Some notable spectral sequences are:

=== Topology and geometry ===

* [[Atiyah–Hirzebruch spectral sequence]] of an [[extraordinary cohomology theory]]
*[[Bar spectral sequence]] for the homology of the classifying space of a group.
*[[Bockstein spectral sequence]] relating the homology with mod ''p'' coefficients and the homology reduced mod ''p''.
*[[Cartan–Leray spectral sequence]] converging to the homology of a quotient space.
*[[Eilenberg–Moore spectral sequence]] for the [[singular cohomology]] of the [[pullback]] of a [[fibration]]
*[[Serre spectral sequence]] of a [[fibration]]

=== Homotopy theory ===

* [[Adams spectral sequence]] in [[stable homotopy theory]]
*[[Adams–Novikov spectral sequence]], a generalization to [[extraordinary cohomology theory|extraordinary cohomology theories]].
*[[Barratt spectral sequence]] converging to the homotopy of the initial space of a cofibration.
*[[Bousfield–Kan spectral sequence]] converging to the homotopy colimit of a functor.
*[[Chromatic spectral sequence]] for calculating the initial terms of the [[Adams–Novikov spectral sequence]].
*[[Cobar spectral sequence]]
*[[EHP spectral sequence]] converging to [[stable homotopy groups of spheres]]
*[[Federer spectral sequence]] converging to homotopy groups of a function space.
*[[Homotopy fixed point spectral sequence]]<ref>{{cite journal |arxiv=math/0406081|first1=Robert R. |last1=Bruner |first2=John |last2=Rognes |title=Differentials in the homological homotopy fixed point spectral sequence |journal=Algebr. Geom. Topol. |volume=5 |issue=2 |date=2005 |pages=653–690 |doi=10.2140/agt.2005.5.653 |doi-access=free}}</ref>
*[[Hurewicz spectral sequence]] for calculating the homology of a space from its homotopy.
*[[Miller spectral sequence]] converging to the mod ''p'' stable homology of a space.
*[[Milnor spectral sequence]] is another name for the [[bar spectral sequence]].
*[[Moore spectral sequence]] is another name for the bar spectral sequence.
*[[Quillen spectral sequence]] for calculating the homotopy of a simplicial group.
*[[Rothenberg–Steenrod spectral sequence]] is another name for the bar spectral sequence.
*[[van Kampen spectral sequence]] for calculating the homotopy of a wedge of spaces.

=== Algebra ===

* [[Čech-to-derived functor spectral sequence]] from [[Čech cohomology]] to [[sheaf cohomology]].
* [[Change of rings spectral sequence]]s for calculating Tor and Ext groups of modules.
* [[Connes spectral sequence]]s converging to the cyclic homology of an algebra.
* [[Gersten–Witt spectral sequence]]
*[[Green's spectral sequence]] for [[Koszul cohomology]]
*[[Grothendieck spectral sequence]] for composing [[derived functor]]s
*[[Hyperhomology spectral sequence]] for calculating hyperhomology.
*[[Künneth spectral sequence]] for calculating the homology of a tensor product of differential algebras.
*[[Leray spectral sequence]] converging to the cohomology of a sheaf.
*[[Local-to-global Ext spectral sequence]]
*[[Lyndon–Hochschild–Serre spectral sequence]] in [[group cohomology|group (co)homology]]
*[[May spectral sequence]] for calculating the Tor or Ext groups of an algebra.
*Spectral sequence of a differential filtered group: described in this article.
*Spectral sequence of a double complex: described in this article.
*Spectral sequence of an exact couple: described in this article.
*[[Universal coefficient spectral sequence]]
*[[van Est spectral sequence]] converging to relative Lie algebra cohomology.

=== Complex and algebraic geometry ===
*[[Arnold's spectral sequence]] in [[singularity theory]].
*[[Bloch–Lichtenbaum spectral sequence]] converging to the algebraic K-theory of a field.
*[[Frölicher spectral sequence]] starting from the [[Dolbeault cohomology]] and converging to the [[algebraic de Rham cohomology]] of a variety.
*[[Hodge–de Rham spectral sequence]] converging to the [[algebraic de Rham cohomology]] of a variety.
*[[Motivic-to-K-theory spectral sequence|Motivic-to-''K''-theory spectral sequence]]