Complete intersections and mod p cochains

TL;DR

This paper develops homotopy invariant definitions for properties of complete intersections in the context of mod p cochains on spaces, exploring their relationships and applications to classifying spaces of groups.

Contribution

It introduces new homotopy invariant characterizations of complete intersection properties for mod p cochains, extending classical and rational cases to a topological setting.

Findings

Suitable versions of properties are equivalent

The first property is stronger than the others

Applications to classifying spaces of groups

Abstract

We give homotopy invariant definitions corresponding to three well known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod p cochains on a space, showing that suitable versions of the second and third are equivalent and that the first is stronger. We are particularly interested in classifying spaces of groups, and we give a number of examples. This paper follows on from arXiv:0906.4025 which considered the classical case of a commutative ring and arXiv:0906.3247 which considered the case of rational homotopy theory.