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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A topological interpretation for the bias invariant


Author: Micheal Dyer
Journal: Proc. Amer. Math. Soc. 98 (1986), 519-523
MSC: Primary 57M20; Secondary 55P15
MathSciNet review: 857954
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0857954-1
PII: S 0002-9939(1986)0857954-1
Keywords: Homotopy type of $ 2$-complexes, homotopy type of $ (\pi ,m)$-complexes, bias invariant
Article copyright: © Copyright 1986 American Mathematical Society