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2005 A stably free nonfree module and its relevance for homotopy classification, case $Q_{28}$
F Rudolf Beyl, Nancy Waller
Algebr. Geom. Topol. 5(3): 899-910 (2005). DOI: 10.2140/agt.2005.5.899

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.

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F Rudolf Beyl. Nancy Waller. "A stably free nonfree module and its relevance for homotopy classification, case $Q_{28}$." Algebr. Geom. Topol. 5 (3) 899 - 910, 2005. https://doi.org/10.2140/agt.2005.5.899

Information

Received: 10 February 2005; Accepted: 1 June 2005; Published: 2005
First available in Project Euclid: 20 December 2017

zbMATH: 1084.57003
MathSciNet: MR2171797
Digital Object Identifier: 10.2140/agt.2005.5.899

Subjects:
Primary: 57M20
Secondary: 19A13, 55P15

Rights: Copyright © 2005 Mathematical Sciences Publishers

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