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Transactions of the American Mathematical Society

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

 

 

On the homotopy of finite $ {CW}$-complexes with polycyclic fundamental group


Author: Mihai Damian
Journal: Trans. Amer. Math. Soc. 361 (2009), 1791-1809
MSC (2000): Primary 57R70, 55P15, 57Q10
DOI: https://doi.org/10.1090/S0002-9947-08-04632-1
Published electronically: October 30, 2008
MathSciNet review: 2465817
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Abstract: Let $ X$ be a finite connected CW-complex of dimension $ q$. If its fundamental group $ \pi_1(X)$ is polycyclic of Hirsch number $ h>q$, we show that at least one homotopy group $ \pi_{i}(X)$ is not finitely generated. If $ h=q$ or $ h=q-1$ the same conclusion holds unless $ X$ is an Eilenberg-MacLane space $ K(\pi_1(X),1)$.


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Additional Information

Mihai Damian
Affiliation: Irma, Université Louis Pasteur, 7, rue René Descartes, 67 084 Strasbourg, France
Email: damian@math.u-strasbg.fr

DOI: https://doi.org/10.1090/S0002-9947-08-04632-1
Keywords: Novikov homology, closed $1$-forms, CW-complexes, homotopy groups
Received by editor(s): January 26, 2007
Published electronically: October 30, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.