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Classifications of 2-complexes whose finite fundamental group is that of a 3-manifold

Published online by Cambridge University Press:  20 January 2009

F. Rudolf Beyl ,
M. Paul Latiolais  and
Nancy Waller
F. Rudolf Beyl
Affiliation:
Department of Mathematical Sciences, Portland State University, Portland, OR 97207-0751, U.S.A.
M. Paul Latiolais
Affiliation:
Department of Mathematical Sciences, Portland State University, Portland, OR 97207-0751, U.S.A.
Nancy Waller
Affiliation:
Department of Mathematical Sciences, Portland State University, Portland, OR 97207-0751, U.S.A.
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Abstract

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We consider spines of spherical space forms; i.e., spines of closed oriented 3-manifolds whose universal cover is the 3-sphere. We give sufficient conditions for such spines to be homotopy or simple homotopy equivalent to 2-complexes with the same fundamental group G and minimal Euler characteristic 1. If the group ring ℤG satisfies stably-free cancellation, then any such 2-complex is homotopy equivalent to a spine of a 3-manifold. If K1(ℤG) is represented by units and K is homotopy equivalent to a spine X, then K and X are simple homotopy equivalent. We exhibit several infinite families of non-abelian groups G for which these conditions apply.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 69 - 84
Copyright
Copyright © Edinburgh Mathematical Society 1997

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