We prove a necessary condition for the existence of an Ap–structure on modp spaces, and also derive a simple proof for the finiteness of the number of modp Ap–spaces of given rank. As a direct application, we compute a list of possible types of rank 3 modp homotopy associative H–spaces.
Keywords: $A_p$-space, $\psi$-operation, homotopy associative $H$-space, Steenrod powers, Adem relations
Huang, Ruizhi 1 ; Wu, Jie 1
@article{10_2140_agt_2017_17_2125,
author = {Huang, Ruizhi and Wu, Jie},
title = {On mod p {Ap{\textendash}spaces}},
journal = {Algebraic and Geometric Topology},
pages = {2125--2144},
year = {2017},
volume = {17},
number = {4},
doi = {10.2140/agt.2017.17.2125},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2017.17.2125/}
}
Huang, Ruizhi; Wu, Jie. On mod p Ap–spaces. Algebraic and Geometric Topology, Tome 17 (2017) no. 4, pp. 2125-2144. doi: 10.2140/agt.2017.17.2125
[1] , On the non-existence of elements of Hopf invariant one, Ann. of Math. 72 (1960) 20 | DOI
[2] , The sphere, considered as an H–space modp, Quart. J. Math. Oxford. Ser. 12 (1961) 52 | DOI
[3] , H–spaces with few cells, Topology 1 (1962) 67 | DOI
[4] , , K–theory and the Hopf invariant, Quart. J. Math. Oxford Ser. 17 (1966) 31 | DOI
[5] , Power operations in K–theory, Quart. J. Math. Oxford Ser. 17 (1966) 165 | DOI
[6] , , Homotopy types within a rational homotopy type, Topology 13 (1974) 209 | DOI
[7] , , Sphere bundles over spheres and H–spaces, Topology 8 (1969) 115 | DOI
[8] , , , , , Rank p− 1 mod-p H–spaces, Israel J. Math. 194 (2013) 641 | DOI
[9] , Local spaces with three cells as H–spaces, Canad. J. Math. 31 (1979) 1293 | DOI
[10] , The mod 3 homotopy type of F4, from: "Localization in group theory and homotopy theory, and related topics" (editor P Hilton), Lecture Notes in Math. 418, Springer (1974) 58
[11] , , Evaluating a pth order cohomology operation, Publ. Mat. 32 (1988) 61 | DOI
[12] , Homotopy associative finite H–spaces and the mod 3 reduced power operations, Publ. Res. Inst. Math. Sci. 23 (1987) 1071 | DOI
[13] , On exterior An–spaces and modified projective spaces, Hiroshima Math. J. 24 (1994) 583
[14] , Mod p decompositions of mod p finite H–spaces, Mem. Fac. Sci. Kochi Univ. Ser. A Math. 22 (2001) 59
[15] , Generalized cohomology operations and H–spaces of low rank, Trans. Amer. Math. Soc. 141 (1969) 335 | DOI
[16] , , The number of mod p A(p)–spaces, Illinois J. Math. 33 (1989) 162
[17] , On the K–ring structure of X–projective n–space, Mem. Fac. Sci. Kyushu Univ. Ser. A 38 (1984) 285 | DOI
[18] , Mod p decompositions of H–spaces ; another approach, Pacific J. Math. 87 (1980) 373 | DOI
[19] , , , On the classification of H–spaces of rank 2, J. Math. Kyoto Univ. 13 (1973) 611 | DOI
[20] , , , Mod p decomposition of compact Lie groups, Publ. Res. Inst. Math. Sci. 13 (1977/78) 627 | DOI
[21] , Homotopy associativity of H–spaces, I, Trans. Amer. Math. Soc. 108 (1963) 275 | DOI
[22] , Homotopy associativity of H–spaces, II, Trans. Amer. Math. Soc. 108 (1963) 293 | DOI
[23] , The mod p decomposition of Lie groups, from: "Localization in group theory and homotopy theory, and related topics" (editor P Hilton), Lecture Notes in Math. 418, Springer (1974) 142
[24] , K–theory operations in mod p loop spaces, Math. Z. 132 (1973) 29 | DOI
[25] , Spheres which are loop spaces mod p, Proc. Amer. Math. Soc. 39 (1973) 616 | DOI
[26] , Mod p decomposition of mod p H–spaces, from: "Algebraic and geometrical methods in topology" (editor L F McAuley), Lecture Notes in Math. 428, Springer (1974) 52 | DOI
[27] , Homotopy associativity and finite CW complexes, Topology 9 (1970) 121 | DOI
[28] , The classification of simply connected H–spaces with three cells, I, Math. Scand. 30 (1972) 193 | DOI
[29] , The classification of simply connected H–spaces with three cells, II, Math. Scand. 30 (1972) 211 | DOI
[30] , On the realization of invariant subgroups of π∗(X), Trans. Amer. Math. Soc. 285 (1984) 467 | DOI
Cité par Sources :