A topological interpretation for the bias invariant

Dyer, Micheal

doi:10.1090/S0002-9939-1986-0857954-1

A topological interpretation for the bias invariant
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Proc. Amer. Math. Soc. 98 (1986), 519-523 Request permission

Abstract:

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

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