The D(2)–problem for dihedral groups of order 4n
Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 2287-2297
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2012.12.2287
Classification : 57M05, 55P15
Keywords: $D(2)$–problem, algebraic 2–complex, $k$–invariant

O’Shea, Seamus  1

1 Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, United Kingdom
@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/}
}
TY  - JOUR
AU  - O’Shea, Seamus
TI  - The D(2)–problem for dihedral groups of order 4n
JO  - Algebraic and Geometric Topology
PY  - 2012
SP  - 2287
EP  - 2297
VL  - 12
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.2287/
DO  - 10.2140/agt.2012.12.2287
ID  - 10_2140_agt_2012_12_2287
ER  - 
%0 Journal Article
%A O’Shea, Seamus
%T The D(2)–problem for dihedral groups of order 4n
%J Algebraic and Geometric Topology
%D 2012
%P 2287-2297
%V 12
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.2287/
%R 10.2140/agt.2012.12.2287
%F 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] W J Browning, Homotopy types of certain finite CW–complexes with finite fundamental group, PhD thesis, Cornell University (1978)

[2] P J Davis, Circulant matrices, Wiley–Interscience (1979)

[3] S Endô, T Miyata, On the class groups of dihedral groups, J. Algebra 63 (1980) 548

[4] K W Gruenberg, Homotopy classes of truncated projective resolutions, Comment. Math. Helv. 68 (1993) 579

[5] M Gutierrez, M P Latiolais, Partial homotopy type of finite two-complexes, Math. Z. 207 (1991) 359

[6] I Hambleton, M Kreck, Cancellation of lattices and finite two-complexes, J. Reine Angew. Math. 442 (1993) 91

[7] F E A Johnson, Stable modules and the D(2)–problem, 301, Cambridge Univ. Press (2003)

[8] M P Latiolais, When homology equivalence implies homotopy equivalence for 2–complexes, J. Pure Appl. Algebra 76 (1991) 155

[9] W H Mannan, The D(2) property for D8, Algebr. Geom. Topol. 7 (2007) 517

[10] W H Mannan, Realizing algebraic 2–complexes by cell complexes, Math. Proc. Cambridge Philos. Soc. 146 (2009) 671

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

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

Cité par Sources :