Spectral Sequences - Further Examples

Further Examples

Some notable spectral sequences are:

• Adams spectral sequence in stable homotopy theory
• Adams–Novikov spectral sequence, a generalization to extraordinary cohomology theories.
• Atiyah–Hirzebruch spectral sequence of an extraordinary cohomology theory
• Bar spectral sequence for the homology of the classifying space of a group.
• Barratt spectral sequence converging to the homotopy of the initial space of a cofibration.
• Bloch–Lichtenbaum spectral sequence converging to the algebraic K-theory of a field.
• Bockstein spectral sequence relating the homology with mod p coefficients and the homology reduced mod p.
• Bousfield–Kan spectral sequence converging to the homotopy colimit of a functor.
• Cartan–Leray spectral sequence converging to the homology of a quotient space.
• Čech-to-derived functor spectral sequence from Čech cohomology to sheaf cohomology.
• Change of rings spectral sequences for calculating Tor and Ext groups of modules.
• Chromatic spectral sequence for calculating the initial terms of the Adams–Novikov spectral sequence.
• Connes spectral sequences converging to the cyclic homology of an algebra.
• EHP spectral sequence converging to stable homotopy groups of spheres
• Eilenberg–Moore spectral sequence for the singular cohomology of the pullback of a fibration
• Federer spectral sequence converging to homotopy groups of a function space.
• Frölicher spectral sequence starting from the Dolbeault cohomology and converging to the algebraic de Rham cohomology of a variety.
• Green's spectral sequence for Koszul cohomology
• Grothendieck spectral sequence for composing derived functors
• Hodge–de Rham spectral sequence converging to the algebraic de Rham cohomology of a variety.
• Hurewicz spectral sequence for calculating the homology of a space from its homotopy.
• Hyperhomology spectral sequence for calculating hyper homology.
• Künneth spectral sequence for calculating the homology of a tensor product of differential algebras.
• Leray spectral sequence converging to the cohomology of a sheaf.
• Leray–Serre spectral sequence of a fibration
• Lyndon–Hochschild–Serre spectral sequence in group (co)homology
• May spectral sequence for calculating the Tor or Ext groups of an algebra.
• 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.
• 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.
• van Kampen spectral sequence for calculating the homotopy of a wedge of spaces.