Homotopy groups

General Introduction
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Online References
Serre: Bourbaki exp 44: Homotopy groups
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
Curtis: Some relations between homotopy and homology, Ann of Math 1965, showed that "the homotopy groups of a finite, simply connected simplicial complex are finitely computable".
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Other Information
A PIalgebra is the algebraic structure looking like the homotopy groups of a space, roughly. This means it is a graded group with Whitehead products, compositions, and action of the fundamental group. See papers by Dwyer. Can define Quillen homology and cohomology of such a thing.
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