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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

On finitely dominated CW complexes


Author: Jerzy Dydak
Journal: Proc. Amer. Math. Soc. 84 (1982), 275-279
MSC: Primary 55P15; Secondary 55S99
MathSciNet review: 637183
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Abstract: Let $ \mathcal{D}$ be the class of all CW complexes homotopy dominated by finite CW complexes. In this paper we prove the following theorem.

Theorem. Suppose a connected CW complex $ X \in \mathcal{D}$ is a union of two connected subcomplexes $ {X_1}$, $ {X_2}$ with $ {X_1} \cap {X_2} = {X_0} \in \mathcal{D}$. Then $ {X_1}$, $ {X_2} \in \mathcal{D}$ if one of the following conditions is satisfied:

(i) $ {\pi _1}({X_0},x) \to {\pi _1}(X,x)$ is a monomorphism for each $ x \in {X_0}$,

(ii) $ {\pi _1}({X_i}) \to {\pi _1}(X)$ is a monomorphism for $ i = 1,2$ and $ {\pi _1}({X_1})$, $ {\pi _1}({X_2})$ are finitely presented.


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

  • [1] Roger C. Lyndon and Paul E. Schupp, Combinatorial group theory, Springer-Verlag, Berlin-New York, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89. MR 0577064
  • [2] Micheal Mather, Counting homotopy types of manifolds, Topology 3 (1965), 93–94. MR 0176470
  • [3] B. H. Neumann, An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London. Ser. A. 246 (1954), 503–554. MR 0062741
  • [4] L. C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension greater than five, Thesis, Princeton University, 1965.
  • [5] C. T. C. Wall, Finiteness conditions for 𝐶𝑊-complexes, Ann. of Math. (2) 81 (1965), 56–69. MR 0171284

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0637183-3
Keywords: Finitely dominated CW complexes, free products with amalgamation
Article copyright: © Copyright 1982 American Mathematical Society