A stably free nonfree module and its relevance for homotopy classification, case Q_{28}

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.

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-37.abs.html

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• An exotic presentation of Q_28
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