Algebraic invariants for homotopy types
Algebraic Topology
2009-10-31 v1
Abstract
We define inductively a sequence of purely algebraic invariants - namely, classes in the Quillen cohomology of the Pi-algebra \pi_* 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.
Cite
@article{arxiv.math/9812035,
title = {Algebraic invariants for homotopy types},
author = {David Blanc},
journal= {arXiv preprint arXiv:math/9812035},
year = {2009}
}