A topological interpretation for the bias invariant

Abstract

The bias invariant has been used to distinguish between the homotopy types of 2 2 -complexes. In this note we show that two finite, connected 2 2 -complexes X X and Y Y with isomorphic fundamental groups and the same Euler characteristic have the same bias invariant if and only if there is a map f : X → Y f:X \to Y which is a homology equivalence π 1 f {\pi _1}f and H 2 f {H_2}f are isomorphisms).