Volume 8, issue 1 (2008)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 23
Issue 9, 3909–4400
Issue 8, 3417–3908
Issue 7, 2925–3415
Issue 6, 2415–2924
Issue 5, 1935–2414
Issue 4, 1463–1934
Issue 3, 963–1462
Issue 2, 509–962
Issue 1, 1–508

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
Examples of exotic free $2$–complexes and stably free nonfree modules for quaternion groups

F Rudolf Beyl and Nancy Waller

Algebraic & Geometric Topology 8 (2008) 1–17
Bibliography
1 P H Berridge, M J Dunwoody, Nonfree projective modules for torsion-free groups, J. London Math. Soc. $(2)$ 19 (1979) 433 MR540056
2 F R Beyl, M P Latiolais, N Waller, Classifications of $2$-complexes whose finite fundamental group is that of a $3$-manifold, Proc. Edinburgh Math. Soc. $(2)$ 40 (1997) 69 MR1437812
3 F R Beyl, N Waller, A stably free nonfree module and its relevance for homotopy classification, case $Q_{28}$, Algebr. Geom. Topol. 5 (2005) 899 MR2171797
4 W J Browning, Homotopy types of certain finite CW-complexes with finite fundamental group, PhD thesis, Cornell University (1979)
5 F E Diederichsen, Über die Ausreduktion ganzzahliger Gruppendarstellungen bei arithmetischer Äquivalenz, Abh. Math. Sem. Hansischen Univ. 13 (1940) 357 MR0002133
6 J Harlander, J A Jensen, Exotic relation modules and homotopy types for certain 1-relator groups, Algebr. Geom. Topol. 6 (2006) 2163 MR2263062
7 C Hog-Angeloni, W Metzler, A J Sieradski, editors, Two-dimensional homotopy and combinatorial group theory, London Mathematical Society Lecture Note Series 197, Cambridge University Press (1993) MR1279174
8 F E A Johnson, Stable modules and the $\mathrm{D}(2)$–problem, London Mathematical Society Lecture Note Series 301, Cambridge University Press (2003) MR2012779
9 F E A Johnson, Stable modules and Wall's $\mathrm{D}(2)$–problem, Comment. Math. Helv. 78 (2003) 18 MR1966750
10 F E A Johnson, Minimal 2-complexes and the $\mathrm{D}(2)$–problem, Proc. Amer. Math. Soc. 132 (2004) 579 MR2022384
11 I Kaplansky, Fields and rings, The University of Chicago Press, Chicago, Ill.-London (1969) MR0269449
12 J Lewin, Projective modules over group-algebras of torsion-free groups, Michigan Math. J. 29 (1982) 59 MR646371
13 B Magurn, R Oliver, L Vaserstein, Units in Whitehead groups of finite groups, J. Algebra 84 (1983) 324 MR723396
14 M S Montgomery, Left and right inverses in group algebras, Bull. Amer. Math. Soc. 75 (1969) 539 MR0238967
15 D S Passman, The algebraic structure of group rings, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons] (1977) MR470211
16 A J Sieradski, M N Dyer, Distinguishing arithmetic for certain stably isomorphic modules, J. Pure Appl. Algebra 15 (1979) 199 MR535186
17 R G Swan, Periodic resolutions for finite groups, Ann. of Math. $(2)$ 72 (1960) 267 MR0124895
18 R G Swan, Projective modules over group rings and maximal orders, Ann. of Math. $(2)$ 76 (1962) 55 MR0139635
19 R G Swan, $K$–theory of finite groups and orders, Lecture Notes in Mathematics 149, Springer (1970) MR0308195
20 R G Swan, Projective modules over binary polyhedral groups, J. Reine Angew. Math. 342 (1983) 66 MR703486
21 M F Vignéras, Simplification pour les ordres des corps de quaternions totalement définis, J. Reine Angew. Math. 286/287 (1976) 257 MR0429841
22 C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. $(2)$ 81 (1965) 56 MR0171284
23 C T C Wall, Finiteness conditions for CW–complexes II, Proc. Roy. Soc. Ser. A 295 (1966) 129 MR0211402