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Inverse limits which are not hereditarily indecomposable


Authors: Alice Mason, John J. Walsh and David C. Wilson
Journal: Proc. Amer. Math. Soc. 83 (1981), 403-407
MSC: Primary 54F15; Secondary 57Q99
DOI: https://doi.org/10.1090/S0002-9939-1981-0624941-3
MathSciNet review: 624941
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Abstract: Let $ X$ be the limit of an inverse sequence $ \left\{ {M_i^n,{f_i}} \right\}$ of closed, connected PL $ n$-manifolds with $ n \geqslant 2$. It is shown that if either (1) each $ M_i^n$ is orientable, each $ {f_i}$ has nonzero degree, and $ {\sup _i}\left\{ {{\text{rank}}\;{H_1}(M_i^n,{\mathbf{Z}})} \right\} < \infty ... ...\;{\text{(2)}}\;{\text{de}}{{\text{g}}_{{\mathbf{Z}}/2{\mathbf{Z}}}}{f_i} \ne 0$ for each $ i$ and $ {\sup _i}\left\{ {{\text{rank}}\;{H_1}(M_i^n,{\mathbf{Z}}/2{\mathbf{Z}})} \right\} < \infty $, then $ X$ is not hereditarily indecomposable.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0624941-3
Keywords: Inverse limit, hereditarily indecomposable, degree
Article copyright: © Copyright 1981 American Mathematical Society

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