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

Volume 26
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
Suspension splittings of $5$-dimensional Poincaré duality complexes and their applications

Steven Amelotte, Tyrone Cutler and Tseleung So

Algebraic & Geometric Topology 26 (2026) 283–319
Bibliography
1 N A’Campo, D Kotschick, Contact structures, foliations, and the fundamental group, Bull. London Math. Soc. 26 (1994) 102 MR1246478
2 M Arkowitz, Introduction to homotopy theory, Springer (2011) MR2814476
3 D Barden, Simply connected five-manifolds, Ann. of Math. (2) 82 (1965) 365 MR184241
4 H J Baues, Homotopy type and homology, Oxford University Press (1996) MR1404516
5 K Borsuk, Sur les groupes des classes de transformations continues, C. R. Acad. Sci. Paris 202 (1936) 1400
6 E H Brown Jr., The cohomology of BSOn and BOn with integer coefficients, Proc. Amer. Math. Soc. 85 (1982) 283 MR652459
7 S Choi, S Kaji, S Theriault, Homotopy decomposition of a suspended real toric space, Bol. Soc. Mat. Mex. (3) 23 (2017) 153 MR3633130
8 T Cutler, T So, The homotopy type of a once-suspended 6-manifold and its applications, Topology Appl. 318 (2022) 108213 MR4467248
9 S Gitler, J D Stasheff, The first exotic class of BF, Topology 4 (1965) 257 MR180985
10 I Hambleton, Y Su, On certain 5-manifolds with fundamental group of order 2, Q. J. Math. 64 (2013) 149 MR3032093
11 J R Harper, Secondary cohomology operations, 49, Amer. Math. Soc. (2002) MR1913285
12 S Hasui, D Kishimoto, T Sato, p-local stable splitting of quasitoric manifolds, Osaka J. Math. 53 (2016) 843 MR3533472
13 R Huang, Homotopy of gauge groups over non-simply connected five-dimensional manifolds, Sci. China Math. 64 (2021) 1061 MR4249235
14 R Huang, Homotopy of gauge groups over high-dimensional manifolds, Proc. Roy. Soc. Edinburgh Sect. A 152 (2022) 182 MR4383247
15 R Huang, Suspension homotopy of 6-manifolds, Algebr. Geom. Topol. 23 (2023) 439 MR4568008
16 R Huang, P Li, Suspension splitting and cohomotopy sets of simply connected 7-manifolds, Canadian Journal of Mathematics (2025) 1
17 I M James, J H C Whitehead, The homotopy theory of sphere bundles over spheres, I, Proc. London Math. Soc. (3) 4 (1954) 196 MR61838
18 M Jung, T O Rot, A geometric computation of cohomotopy groups in codegree one, Algebr. Geom. Topol. 25 (2025) 3603 MR4972721
19 S Kaji, S Theriault, Suspension splittings and self-maps of flag manifolds, Acta Math. Sin. (Engl. Ser.) 35 (2019) 445 MR3928400
20 R Kirby, P Melvin, P Teichner, Cohomotopy sets of 4-manifolds, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18, Geom. Topol. Publ. (2012) 161 MR3084237
21 P Konstantis, Vector bundles and cohomotopies of spin 5-manifolds, Homology Homotopy Appl. 23 (2021) 143 MR4145999
22 M Kreck, Y Su, On 5-manifolds with free fundamental group and simple boundary links in S5, Geom. Topol. 21 (2017) 2989 MR3687112
23 P Li, Homotopy types of suspended 4-manifolds, Algebr. Geom. Topol. 24 (2024) 2933 MR4790757
24 P Li, J Pan, J Wu, On modular cohomotopy groups, Israel J. Math. 253 (2023) 887 MR4575431
25 P Li, Z Zhu, The homotopy decomposition of the suspension of a non-simply-connected five-manifold, Proc. Royal Soc. Edin. Sec. A Math (2024)
26 I Madsen, R J Milgram, The classifying spaces for surgery and cobordism of manifolds, 92, Princeton Univ. Press (1979) MR548575
27 J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
28 R E Mosher, M C Tangora, Cohomology operations and applications in homotopy theory, Harper & Row (1968) MR226634
29 F P Peterson, Generalized cohomotopy groups, Amer. J. Math. 78 (1956) 259 MR84136
30 S Smale, On the structure of manifolds, Amer. J. Math. 84 (1962) 387 MR153022
31 T So, S Theriault, The suspension of a 4-manifold and its applications, Israel J. Math. 265 (2025) 115 MR4870828
32 E Spanier, Borsuk’s cohomotopy groups, Ann. of Math. (2) 50 (1949) 203 MR29170
33 N E Steenrod, Products of cocycles and extensions of mappings, Ann. of Math. (2) 48 (1947) 290 MR22071
34 R Stöcker, On the structure of 5-dimensional Poincaré duality spaces, Comment. Math. Helv. 57 (1982) 481 MR689075
35 L R Taylor, The principal fibration sequence and the second cohomotopy set, from: "Proceedings of the Freedman Fest" (editors R Kirby, V Krushkal, Z Wang), Geom. Topol. Monogr. 18, Geom. Topol. Publ. (2012) 235 MR3084240
36 J Wu, Homotopy theory of the suspensions of the projective plane, 769 (2003) MR1955357
37 A V Zhubr, On a paper by Barden, J. Math. Sci. 119 (2004) 35