nLab spectral sequence of a tower of fibrations

Idea

Given a tower of fibrations of homotopy types, its degreewise homotopy groups naturally form an exact couple. The induced spectral sequence is the spectral sequence of the tower.

tower diagram/filtering	spectral sequence of a filtered stable homotopy type
filtered chain complex	spectral sequence of a filtered complex
Postnikov tower	Atiyah-Hirzebruch spectral sequence
chromatic tower	chromatic spectral sequence
skeleta of simplicial object	spectral sequence of a simplicial stable homotopy type
skeleta of Sweedler coring of E-∞ algebra	Adams spectral sequence
filtration by support	…
slice filtration	slice spectral sequence

Related concepts

filtered objects

• filtered topological space

  • spectral sequence of a tower of fibrations

• filtered vector space

• filtered chain complex

  • spectral sequence of a filtered complex

  • Hodge filtration

• filtered ring

• filtered object in an (∞,1)-category

• filtered stable homotopy type

  • spectral sequence of a filtered stable homotopy type

associated graded objects

• associated graded vector space

• associated graded ring

References

• Paul Goerss, Rick Jardine, section VI.2 (in the 1999 version) or section VII.6 (in the 1996 version) of Simplicial homotopy theory

• Mike Shulman, spectral sequences (2013)