Algebraic & Geometric Topology 5 (2005) 899–910

DOI: 10.2140/agt.2005.5.899

arXiv: math.RA/0508196

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

Mathematical Subject Classification

Primary: 57M20

Secondary: 19A13, 55P15

References

Forward citations

Publication

Received: 10 February 2005
Accepted: 1 June 2005
Published: 29 July 2005

Authors