Geodesic
A stably free nonfree module and its relevance for homotopy classification, case Q28
Beyl, F Rudolf1 ; Waller, Nancy1
1Department of Mathematics and Statistics, Portland State University, Portland OR 97207-0751, USA
Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 899-910
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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.

DOI : 10.2140/agt.2005.5.899
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

Beyl, F Rudolf  1   ; Waller, Nancy  1

1 Department of Mathematics and Statistics, Portland State University, Portland OR 97207-0751, USA 
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Beyl, F Rudolf; Waller, Nancy. A stably free nonfree module and its relevance for homotopy classification, case Q28. Algebraic and Geometric Topology, Tome 5 (2005) no. 3, pp. 899-910. doi: 10.2140/agt.2005.5.899

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