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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Trees of homotopy types of 2-dimensional $ {\rm CW}$ complexes. II


Authors: Micheal N. Dyer and Allan J. Sieradski
Journal: Trans. Amer. Math. Soc. 205 (1975), 115-125
MSC: Primary 55D15
MathSciNet review: 0425957
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Abstract: A $ \pi $-complex is a finite, connected $ 2$-dimensional CW complex with fundamental group $ \pi $. The tree HT$ (\pi )$ of homotopy types of $ \pi $-complexes has width $ \leq N$ if there is a root $ Y$ of the tree such that, for any $ \pi $-complex $ X,X \vee ( \vee _{i = 1}^NS_i^2)$ lies on the stalk generated by $ Y$. Let $ \pi $ be a finite abelian group with torsion coefficients $ {\tau _1}, \cdots ,{\tau _n}$. The main theorem of this paper asserts that width HT$ (\pi ) \leq n(n - 1)/2$. This generalizes the results of [4].


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DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0425957-4
PII: S 0002-9947(1975)0425957-4
Article copyright: © Copyright 1975 American Mathematical Society