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Proceedings of the American Mathematical Society
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.

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Additional Information

PII: S 0002-9939(1982)0637183-3
Keywords: Finitely dominated CW complexes, free products with amalgamation
Article copyright: © Copyright 1982 American Mathematical Society