Remote Access Transactions of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 57M20, 57Q10

Retrieve articles in all journals with MSC: 57M20, 57Q10


Additional Information

Article copyright: © Copyright 1986 American Mathematical Society