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spectral sequence of a simplicial stable homotopy type

Contents

Context

Stable Homotopy theory

Homological algebra

homological algebra

(also nonabelian homological algebra)

Introduction

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Contents

Idea

For 𝒞\mathcal{C} a stable (∞,1)-category and X X_\bullet a simplicial object in an (∞,1)-category in 𝒞\mathcal{C}, then the simplicial skeleta of XX give it the structure of a filtered object in an (∞,1)-category. The corresponding spectral sequence of a filtered stable homotopy type has as its first page the Moore complexes of the corresponding simplicial objects of homotopy groups.

Examples

tower diagram/filteringspectral sequence of a filtered stable homotopy type
filtered chain complexspectral sequence of a filtered complex
Postnikov towerAtiyah-Hirzebruch spectral sequence
chromatic towerchromatic spectral sequence
skeleta of simplicial objectspectral sequence of a simplicial stable homotopy type
skeleta of Sweedler coring of E-∞ algebraAdams spectral sequence
filtration by support
slice filtrationslice spectral sequence

References

The general theory is developed in

Quick review is in

Last revised on February 1, 2016 at 16:42:24. See the history of this page for a list of all contributions to it.