Examples of cohomology manifolds which are not homologically locally connected

TL;DR

This paper constructs infinitely many examples of higher-dimensional metrizable cohomology manifolds that are not homologically locally connected, extending Bredon's initial 2-dimensional example to all dimensions n ≥ 3.

Contribution

The authors provide a method to generate infinitely many higher-dimensional cohomology manifolds lacking homological local connectedness, broadening the scope of Bredon's original example.

Findings

Existence of infinitely many such manifolds in all dimensions n ≥ 3

Construction of metrizable examples in each dimension

Extension of Bredon's 2D example to higher dimensions

Abstract

Bredon has constructed a 2-dimensional compact cohomology manifold which is not homologically locally connected, with respect to the singular homology. In the present paper we construct infinitely many such examples (which are in addition metrizable spaces) in all remaining dimensions $n \ge 3$.