Geodesic
The D(2) property for D8
Mannan, W H1
1University College London, Gower Street, London WC1E 6BT, UK
Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 517-528
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Wall’s D(2) problem asks if a cohomologically 2–dimensional geometric 3–complex is necessarily homotopy equivalent to a geometric 2–complex. We solve part of the problem when the fundamental group is dihedral of order 2n and give a complete solution for the case where it is D8 the dihedral group of order 8.

DOI : 10.2140/agt.2007.7.517
Keywords: Wall's D(2) problem, algebraic complexes, k-invariants

Mannan, W H  1

1 University College London, Gower Street, London WC1E 6BT, UK 
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Mannan, W H. The D(2) property for D8. Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 517-528. doi: 10.2140/agt.2007.7.517

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[3] F E A Johnson, Stable modules and the $D(2)$–problem, London Mathematical Society Lecture Note Series 301, Cambridge University Press (2003)

[4] R G Swan, Torsion free cancellation over orders, Illinois J. Math. 32 (1988) 329

[5] C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. (2) 81 (1965) 56

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