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On the homotopy groups of the suspended quaternionic projective plane and applications

Juxin Yang, Juno Mukai and Jie Wu

Algebraic & Geometric Topology 25 (2025) 2981–3033
Bibliography
1 J F Adams, On the groups J(X), I, Topology 2 (1963) 181 MR159336
2 A L Blakers, W S Massey, The homotopy groups of a triad, Proc. Nat. Acad. Sci. U.S.A. 35 (1949) 322 MR30757
3 E Dror Farjoun, Fundamental group of homotopy colimits, Adv. Math. 182 (2004) 1 MR2028495
4 R Fritsch, R A Piccinini, Cellular structures in topology, 19, Cambridge Univ. Press (1990) MR1074175
5 B Gray, On the homotopy groups of mapping cones, Proc. Lond. Math. Soc. 26 (1973) 497 MR334198
6 A Hatcher, Algebraic topology, Cambridge Univ. Press (2002) MR1867354
7 I M James, On the homotopy groups of certain pairs and triads, Q. J. Math. 5 (1954) 260 MR68837
8 I M James, The topology of Stiefel manifolds, 24, Cambridge Univ. Press (1976) MR431239
9 A Liulevicius, A theorem in homological algebra and stable homotopy of projective spaces, Trans. Amer. Math. Soc. 109 (1963) 540 MR156346
10 M E Mahowald, D C Ravenel, Toward a global understanding of the homotopy groups of spheres, from: "The Lefschetz centennial conference, II", Contemp. Math. 58, Amer. Math. Soc. (1987) 57 MR893848
11 M Mimura, On the generalized Hopf homomorphism and the higher composition, II : πn+i(Sn) for i = 21 and 22, J. Math. Kyoto Univ. 4 (1965) 301 MR177413
12 M Mimura, M Mori, N Oda, Determination of 2-components of the 23- and 24-stems in homotopy groups of spheres, Mem. Fac. Sci. Kyushu Univ. Ser. A 29 (1975) 1 MR375300
13 M Mimura, H Toda, The (n+20)-th homotopy groups of n-spheres, J. Math. Kyoto Univ. 3 (1963) 37 MR157384
14 T Miyauchi, J Mukai, Determination of the 2-primary components of the 32-stem homotopy groups of Sn, Bol. Soc. Mat. Mex. 23 (2017) 319 MR3633138
15 J Mukai, The order of the attaching class in the suspended quaternionic quasiprojective space, Publ. Res. Inst. Math. Sci. 20 (1984) 717 MR762951
16 J Mukai, On stable homotopy of the complex projective space, Japan. J. Math. 19 (1993) 191 MR1231514
17 N Oda, Hopf invariants in metastable homotopy groups of spheres, Mem. Fac. Sci. Kyushu Univ. Ser. A 30 (1976) 221 MR420617
18 N Oda, Unstable homotopy groups of spheres, Bull. Inst. Adv. Res. Fukuoka Univ. (1979) 49 MR781607
19 K Ōguchi, Generators of 2-primary components of homotopy groups of spheres, unitary groups and symplectic groups, J. Fac. Sci. Univ. Tokyo Sect. I 11 (1964) 65 MR174055
20 J J Rotman, An introduction to homological algebra, Springer (2009) MR2455920
21 P Selick, S Theriault, J Wu, Functorial decompositions of looped coassociative co-H spaces, Canad. J. Math. 58 (2006) 877 MR2245278
22 P Selick, J Wu, On functorial decompositions of self-smash products, Manuscripta Math. 111 (2003) 435 MR2002820
23 D Sullivan, Genetics of homotopy theory and the Adams conjecture, Ann. of Math. 100 (1974) 1 MR442930
24 H Toda, Generalized Whitehead products and homotopy groups of spheres, J. Inst. Polytech. Osaka City Univ. Ser. A 3 (1952) 43 MR60822
25 H Toda, p-primary components of homotopy groups, IV : Compositions and toric constructions, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 32 (1959) 297 MR111041
26 H Toda, A topological proof of theorems of Bott and Borel–Hirzeburch [sic] for homotopy groups of unitary groups, Mem. Coll. Sci. Univ. Kyoto Ser. A. Math. 32 (1959) 103 MR108790
27 H Toda, Composition methods in homotopy groups of spheres, 49, Princeton Univ. Press (1962) MR143217
28 G W Whitehead, Elements of homotopy theory, 61, Springer (1978) MR516508
29 J H C Whitehead, On adding relations to homotopy groups, Ann. of Math. 42 (1941) 409 MR4123
30 C Wilkerson, Genus and cancellation, Topology 14 (1975) 29 MR367995
31 J Wu, Homotopy theory of the suspensions of the projective plane, 769, Amer. Math. Soc. (2003) MR1955357