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Algebraic invariants for homotopy types

David Blanc
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Abstract

We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra π_* X - for distinguishing between different homotopy types of spaces. Another sequence of such cohomology classes allows one to decide whether a given abstract Pi-algebra can be realized as the homotopy Pi-algebra of a space in the first place. The paper is written for a relatively general "resolution model category", so it also applies, for example, to rational homotopy types.

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David Blanc. 1998-12-07. Algebraic invariants for homotopy types. https://doi.org/10.1017/s030500419900393x

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