Steenrod-Cech homology-cohomology theories associated with bivariant functors

TL;DR

This paper constructs a bivariant functor linking Cech cohomology and Steenrod homology, providing a unified framework for these theories on compact metric spaces.

Contribution

It introduces a specific bivariant functor that relates Cech cohomology with Steenrod homology, expanding the understanding of their connection.

Findings

The bivariant functor successfully models Cech cohomology and Steenrod homology.

The construction applies at least to compact metric spaces.

It extends the framework of bivariant functors to classical homology and cohomology theories.

Abstract

Let NG0 denote the category of all pointed numerically generated spaces and continuous maps preserving base-points. In [SYH], we described a passage from bivariant functors to generalized homology and cohomology theories. In this paper, we construct a bivariant functor such that the associated cohomology is the Cech cohomology and the homology is the Steenrod homology (at least for compact metric spaces).