Algebraic invariants for homotopy types

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.

References in corpus (1)

• CW simplicial resolutions of spaces, with an application to loop spaces

Cited by in corpus (7)

• Quillen model structures for relative homological algebra
• On realizing diagrams of Pi-algebras
• Higher homotopy invariants for spaces and maps
• Higher homotopy operations and André-Quillen cohomology
• CW simplicial resolutions of spaces, with an application to loop spaces
• Spectral Sequences in $(\infty ,1)$-Categories
• The realizability of operations on homotopy groups concentrated in two degrees