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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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  • [SD] A. Sieradski and M. Dyer, Distinguishing arithmetic for certain stably isomorphic modules, J. Pure Appl. Algebra 15 (1979), 199-217. MR 535186 (80k:20007)
  • [D] M. Dyer, Invariants for distinguishing between stably isomorphic modules, J. Pure Appl. Algebra 37 (1985), 117-153. MR 796404 (87f:18009)
  • [WB] W. Browning, Finite CW complexes of cohomological dimension 2 with finite abelian $ {\pi _1}$, preprint, ETH, Zurich, 1979.
  • [Du] M. Dunwoody, The homotopy type of a two-dimensional complex, Bull. London Math. Soc. 8 (1976), 282-285. MR 0425943 (54:13893)
  • [D$ _{2}$] M. Dyer, Homotopy classification of $ (\pi ,m)$-complexes, J. Pure Appl. Algebra 7 (1976), 249-282. MR 0400215 (53:4050)
  • [Sc] J. Schafer, Finite complexes and integral representations. II, Canad. Math. Bull. 27 (1983), 1-7. MR 725244 (85m:55008)
  • [M] W. Metzler, Uber den Homotopietyp zweidimensionaler CW-complexe..., J. Reine Angew. Math. 285 (1976), 7-23. MR 0440527 (55:13402)
  • [S] A. Sieradski, A semigroup of simple homotopy type, Math. Z. 153 (1977), 135-148. MR 0438321 (55:11237)
  • [DS] M. Dyer and A. Sieradski, Trees of homotopy types of two-dimensional CW-complexes, Comment Math. Helv. 48 (1973), 31-44. MR 0377905 (51:14074)

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Keywords: Homotopy type of $ 2$-complexes, homotopy type of $ (\pi ,m)$-complexes, bias invariant
Article copyright: © Copyright 1986 American Mathematical Society

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