Volume 21, issue 4 (2021)

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

Volume 25, 1 issue

Volume 24, 9 issues

Volume 23, 9 issues

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
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
An exotic presentation of $Q_{28}$

Wajid H Mannan and Tomasz Popiel

Algebraic & Geometric Topology 21 (2021) 2065–2084
Bibliography
1 P H Berridge, M J Dunwoody, Nonfree projective modules for torsion-free groups, J. Lond. Math. Soc. 19 (1979) 433 MR540056
2 M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
3 F R Beyl, N Waller, A stably free nonfree module and its relevance for homotopy classification, case Q28, Algebr. Geom. Topol. 5 (2005) 899 MR2171797
4 F R Beyl, N Waller, Examples of exotic free 2–complexes and stably free nonfree modules for quaternion groups, Algebr. Geom. Topol. 8 (2008) 1 MR2377275
5 I Bokor, D Crowley, S Friedl, F Hebestreit, D Kasprowski, M Land, J Nicholson, Connected sum decompositions of high-dimensional manifolds, from: "2019–20 MATRIX annals" (editors D R Wood, J d Gier, C E Praeger, T Tao), Springer (2021) 5
6 W Bosma, J Cannon, C Playoust, The Magma algebra system, I : The user language, J. Symbolic Comput. 24 (1997) 235 MR1484478
7 M R Bridson, M Tweedale, Deficiency and abelianized deficiency of some virtually free groups, Math. Proc. Cambridge Philos. Soc. 143 (2007) 257 MR2364648
8 M J Dunwoody, The homotopy type of a two-dimensional complex, Bull. Lond. Math. Soc. 8 (1976) 282 MR425943
9 T Edwards, Generalised Swan modules and the D(2) problem, Algebr. Geom. Topol. 6 (2006) 71 MR2199454
10 R H Fox, Free differential calculus, V : The Alexander matrices re-examined, Ann. of Math. 71 (1960) 408 MR111781
11 K W Gruenberg, P A Linnell, Generation gaps and abelianized defects of free products, J. Group Theory 11 (2008) 587 MR2446142
12 I Hambleton, Two remarks on Wall’s D2 problem, Math. Proc. Cambridge Philos. Soc. 167 (2019) 361 MR3991378
13 J Harlander, A survey of recent progress on some problems in 2–dimensional topology, from: "Advances in two-dimensional homotopy and combinatorial group theory" (editors W Metzler, S Rosebrock), Lond. Math. Soc. Lect. Note Ser. 446, Cambridge Univ. Press (2018) 1 MR3752465
14 C Hog-Angeloni, Beiträge zum (einfachen) Homotopietyp zweidimensionaler Komplexe zu freien Produkten und anderen gruppentheoretischen Konstruktionen, PhD thesis, Goethe-Universität Frankfurt am Main (1988)
15 F E A Johnson, Explicit homotopy equivalences in dimension two, Math. Proc. Cambridge Philos. Soc. 133 (2002) 411 MR1919714
16 F E A Johnson, Stable modules and the D(2)–problem, 301, Cambridge Univ. Press (2003) MR2012779
17 F E A Johnson, Stable modules and Wall’s D(2)–problem, Comment. Math. Helv. 78 (2003) 18 MR1966750
18 F E A Johnson, Minimal 2–complexes and the D(2)–problem, Proc. Amer. Math. Soc. 132 (2004) 579 MR2022384
19 M P Latiolais, Homotopy and homology classification of 2–complexes, from: "Two-dimensional homotopy and combinatorial group theory" (editors C Hog-Angeloni, W Metzler), Lond. Math. Soc. Lect. Note Ser. 197, Cambridge Univ. Press (1993) 97 MR1279177
20 P A Linnell, Minimal free resolutions and (G,n)–complexes for finite abelian groups, Proc. Lond. Math. Soc. 66 (1993) 303 MR1199069
21 M Lustig, Infinitely many pairwise homotopy inequivalent 2–complexes Ki with fixed π1Ki and χ(Ki), J. Pure Appl. Algebra 88 (1993) 173 MR1233322
22 W H Mannan, The D(2) property for D8, Algebr. Geom. Topol. 7 (2007) 517 MR2308955
23 W H Mannan, Homotopy types of truncated projective resolutions, Homology Homotopy Appl. 9 (2007) 445 MR2366957
24 W H Mannan, Quillen’s plus construction and the D(2) problem, Algebr. Geom. Topol. 9 (2009) 1399 MR2520404
25 W H Mannan, Realizing algebraic 2–complexes by cell complexes, Math. Proc. Cambridge Philos. Soc. 146 (2009) 671 MR2496351
26 W H Mannan, A commutative version of the group ring, J. Algebra 379 (2013) 113 MR3019248
27 W H Mannan, Explicit generators for the relation module in the example of Gruenberg–Linnell, Math. Proc. Cambridge Philos. Soc. 161 (2016) 199 MR3530503
28 W H Mannan, S O’Shea, Minimal algebraic complexes over D4n, Algebr. Geom. Topol. 13 (2013) 3287 MR3248735
29 W Metzler, Über den Homotopietyp zweidimensionaler CW–Komplexe und Elementartransformationen bei Darstellungen von Gruppen durch Erzeugende und definierende Relationen, J. Reine Angew. Math. 285 (1976) 7 MR440527
30 J Nicholson, Cancellation for (G,n)–complexes and the Swan finiteness obstruction, preprint (2020) arXiv:2005.01664
31 J Nicholson, Projective modules and the homotopy classification of (G,n)–complexes, preprint (2020) arXiv:2004.04252
32 J Nicholson, A cancellation theorem for modules over integral group rings, Math. Proc. Cambridge Philos. Soc. (2020)
33 J Nicholson, On CW–complexes over groups with periodic cohomology, Trans. Amer. Math. Soc. (2021)
34 S O’Shea, The D(2)–problem for dihedral groups of order 4n, Algebr. Geom. Topol. 12 (2012) 2287 MR3020207
35 J R Stallings, On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968) 312 MR228573
36 R G Swan, Groups of cohomological dimension one, J. Algebra 12 (1969) 585 MR240177
37 R G Swan, Projective modules over binary polyhedral groups, J. Reine Angew. Math. 342 (1983) 66 MR703486
38 C T C Wall, Finiteness conditions for CW–complexes, Ann. of Math. 81 (1965) 56 MR171284
39 C T C Wall, List of problems, from: "Homological group theory" (editor C T C Wall), London Mathematical Society Lecture Note Series 36, Cambridge Univ. Press (1979) 369 MR564417