Algebraic and Geometric Topology 5 (2005), paper no. 37, pages 899-910.

A stably free nonfree module and its relevance for homotopy classification, case Q_28

F. Rudolf Beyl, Nancy Waller

Abstract. The paper constructs an `exotic' algebraic 2-complex over the generalized quaternion group of order 28, with the boundary maps given by explicit matrices over the group ring. This result depends on showing that a certain ideal of the group ring is stably free but not free. As it is not known whether the complex constructed here is geometrically realizable, this example is proposed as a suitable test object in the investigation of an open problem of C.T.C. Wall, now referred to as the D(2)-problem.

Keywords. Algebraic 2-complex, Wall's D(2)-problem, geometric realization of algebraic 2-complexes, homotopy classification of 2-complexes, generalized quaternion groups, partial projective resolution, stably free nonfree module

AMS subject classification. Primary: 57M20. Secondary: 55P15, 19A13.

E-print: arXiv:math.RA/0508196

DOI: 10.2140/agt.2005.5.899

Submitted: 10 February 2005. Accepted: 1 June 2005. Published: 29 July 2005.

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F. Rudolf Beyl, Nancy Waller
Department of Mathematics and Statistics, Portland State University
Portland, OR 97207-0751, USA
Email: beylf at pdx dot edu

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