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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Simple homotopy type of finite $ 2$-complexes with finite abelian fundamental group


Author: M. Paul Latiolais
Journal: Trans. Amer. Math. Soc. 293 (1986), 655-662
MSC: Primary 57M20; Secondary 57Q10
DOI: https://doi.org/10.1090/S0002-9947-1986-0816317-X
MathSciNet review: 816317
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Abstract: Theorem 1. Let $ K$ be a finite $ 2$-dimensional $ CW$-complex with $ {\pi _1}(K)$ finite and abelian. Then every element of the Whitehead group of $ K$ is realizable as the torsion of a self-homotopy equivalence on $ K$.

Theorem 2. Homotopy equivalence and simple homotopy equivalence are the same for finite $ 2$-dimensional $ CW$-complexes with finite abelian fundamental groups.


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DOI: https://doi.org/10.1090/S0002-9947-1986-0816317-X
Article copyright: © Copyright 1986 American Mathematical Society