We give a full solution in terms of k–invariants of the D(2)–problem for D4n, assuming that Z[D4n] satisfies torsion-free cancellation.
Keywords: $D(2)$–problem, algebraic 2–complex, $k$–invariant
O’Shea, Seamus  1
@article{10_2140_agt_2012_12_2287,
author = {O{\textquoteright}Shea, Seamus},
title = {The {D(2){\textendash}problem} for dihedral groups of order 4n},
journal = {Algebraic and Geometric Topology},
pages = {2287--2297},
year = {2012},
volume = {12},
number = {4},
doi = {10.2140/agt.2012.12.2287},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.2287/}
}
O’Shea, Seamus. The D(2)–problem for dihedral groups of order 4n. Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 2287-2297. doi: 10.2140/agt.2012.12.2287
[1] , Homotopy types of certain finite CW–complexes with finite fundamental group, PhD thesis, Cornell University (1978)
[2] , Circulant matrices, Wiley–Interscience (1979)
[3] , , On the class groups of dihedral groups, J. Algebra 63 (1980) 548
[4] , Homotopy classes of truncated projective resolutions, Comment. Math. Helv. 68 (1993) 579
[5] , , Partial homotopy type of finite two-complexes, Math. Z. 207 (1991) 359
[6] , , Cancellation of lattices and finite two-complexes, J. Reine Angew. Math. 442 (1993) 91
[7] , Stable modules and the D(2)–problem, 301, Cambridge Univ. Press (2003)
[8] , When homology equivalence implies homotopy equivalence for 2–complexes, J. Pure Appl. Algebra 76 (1991) 155
[9] , The D(2) property for D8, Algebr. Geom. Topol. 7 (2007) 517
[10] , Realizing algebraic 2–complexes by cell complexes, Math. Proc. Cambridge Philos. Soc. 146 (2009) 671
[11] , Torsion free cancellation over orders, Illinois J. Math. 32 (1988) 329
[12] , Finiteness conditions for CW–complexes, Ann. of Math. 81 (1965) 56
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