Homotopy classification of higher homotopy commutative loop spaces with finitely generated cohomology
Yusuke Kawamoto
Source: Hiroshima Math. J. Volume 30, Number 2
(2000), 317-344.
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Permanent link to this document: http://projecteuclid.org/euclid.hmj/1206124689
Mathematical Reviews number (MathSciNet): MR1777518
Zentralblatt MATH identifier: 0958.55010
References
[1] J. F. Adams and C. W. Wilkerson, Finite //-spaces and algebras over the Steenrod algebra, Ann. of Math. 111 (1980), 95-143.
Zentralblatt MATH: 0404.55020
Mathematical Reviews (MathSciNet): MR558398
[2] J. Aguade, C. Broto and D. Notbohm, Homotopy classification of spaces with interesting cohomology and a conjecture of Cooke, Part I, Topology 33 (1994), 455-492.
Zentralblatt MATH: 0843.55007
Mathematical Reviews (MathSciNet): MR1286926
[3] A. Bousfield and D. Kan, Homotopy limits, completions and localizations, Springer Lecture Notes in Math. 304 (1972).
Zentralblatt MATH: 0259.55004
Mathematical Reviews (MathSciNet): MR365573
[4] C. Broto and J. A. Crespo, //-spaces with noetherian mod two cohomology algebra, Topology 38 (1999), 353-386.
Zentralblatt MATH: 0927.55017
Mathematical Reviews (MathSciNet): MR1660329
[5] W. Browder, The cohomology of covering spaces of //-spaces, Bull. Amer. Math. Soc. 65 (1959), 140-141.
Zentralblatt MATH: 0088.38802
Mathematical Reviews (MathSciNet): MR111024
[6] W. Browder, Homotopy commutative //-spaces, Ann. of Math. 75 (1962), 283-311.
Zentralblatt MATH: 0138.18503
Mathematical Reviews (MathSciNet): MR150778
[7] A. Clark and J. Ewing, The realization of polynomial algebras as cohomology rings, Pacific J. Math. 50 (1974), 425-434.
Zentralblatt MATH: 0333.55002
Mathematical Reviews (MathSciNet): MR367979
[8] J. A. Crespo, Structure of mod p //-spaces with finiteness conditions, Preprint.
[9] E. Dror Farjoun, Cellular spaces, null spaces and homotopy localization, Springer Lecture Notes in Math. 1622 (1996).
Zentralblatt MATH: 0842.55001
Mathematical Reviews (MathSciNet): MR1392221
[10] W. G. Dwyer, H. R. Miller and C. W. Wilkerson, The homotopical uniqueness of classifying spaces, Topology 31 (1992), 29-45.
Zentralblatt MATH: 0748.55005
Mathematical Reviews (MathSciNet): MR1153237
[11] W. G. Dwyer and C. W. Wilkerson, Homotopy fixed point methods for Lie groups and finite loop spaces, Ann. of Math. 139 (1994), 395-442.
Zentralblatt MATH: 0801.55007
Mathematical Reviews (MathSciNet): MR1274096
[12] W. G. Dwyer and C. W. Wilkerson, Product splittings of p-compact groups, Funct. Math. 147 (1995), 275-300.
Zentralblatt MATH: 0847.55005
Mathematical Reviews (MathSciNet): MR1348723
[13] Y. Hemmi, Higher homotopy commutativity of //-spaces and the mod/? torus theorem, Pacific J. Math. 149 (1991), 95-111.
Zentralblatt MATH: 0691.55007
Mathematical Reviews (MathSciNet): MR1099785
[14] K. Iriye and A. Kono, Mod/7 retracts of G-product spaces, Math. Z. 190 (1985), 357-363.
Zentralblatt MATH: 0554.55004
Mathematical Reviews (MathSciNet): MR806893
[15] R. M. Kane, The homology of Hopf spaces, North-Holland Math. Library 40 (1988).
Zentralblatt MATH: 0651.55001
Mathematical Reviews (MathSciNet): MR961257
[16] Y. Kawamoto, Loop spaces of //-spaces with finitely generated cohomology, Pacific J. Math. 190 (1999), 311-328.
Zentralblatt MATH: 1011.55006
Mathematical Reviews (MathSciNet): MR1722897
[17] Y. Kawamoto and J. P. Lin, Homotopy commutativity of //-spaces with finitely generated cohomology, Preprint.
Zentralblatt MATH: 0977.55005
[18] J. P. Lin, Loops of //-spaces with finitely generated cohomology rings, Topology Appl. 60 (1994), 131-152.
Zentralblatt MATH: 0837.55012
Mathematical Reviews (MathSciNet): MR1302469
[19] J. P. Lin, //-spaces with finiteness conditions, Handbook of Algebraic Topology, edited by I. M. James, North-Holland (1995), 1095-1141.
Zentralblatt MATH: 0941.55002
Mathematical Reviews (MathSciNet): MR1361907
[20] C. McGibbon, Some properties of //-spaces of rank 2, Proc. Amer. Math. Soc. 81 (1981), 121-124.
Zentralblatt MATH: 0475.55007
Mathematical Reviews (MathSciNet): MR589152
[21] C. McGibbon, Homotopy commutativity in localized groups, Amer. J. Math. 106 (1984), 665- 687.
Zentralblatt MATH: 0574.55004
Mathematical Reviews (MathSciNet): MR745146
[22] C. McGibbon, Higher forms of homotopy commutativity and finite loop spaces, Math. Z. 201 (1989), 363-374.
Zentralblatt MATH: 0682.55006
Mathematical Reviews (MathSciNet): MR999733
[23] H. R. Miller, The Sullivan conjecture on maps from classifying spaces, Ann. of Math. 120 (1984), 39-87.
Zentralblatt MATH: 0552.55014
Mathematical Reviews (MathSciNet): MR750716
[24] M. Mimura and H. Toda, Cohomology operations and the homotopy of compact Lie groups-I, Topology 9 (1970), 317-336.
Zentralblatt MATH: 0204.23803
Mathematical Reviews (MathSciNet): MR266237
[25] M. Mimura and H. Toda, Topology of Lie groups, I and II, Trans. Math. Monographs 91 (1991), Amer. Math. Soc.
Zentralblatt MATH: 0757.57001
Mathematical Reviews (MathSciNet): MR1122592
[26] D. Notbohm, Classifying spaces of compact Lie groups and finite loop spaces, Handbook of Algebraic Topology, edited by I. M. James, North-Holland (1995), 1049-1094.
Zentralblatt MATH: 0864.55013
Mathematical Reviews (MathSciNet): MR1361906
[27] D. Notbohm, Topological realization of a family of pseudoreflection groups, Funct. Math. 155 (1998), 1-31.
Zentralblatt MATH: 0896.55013
Mathematical Reviews (MathSciNet): MR1487985
[28] D. Notbohm, Unstable splittings of classifying spaces of /?-compact groups, Preprint.
Zentralblatt MATH: 0954.55013
[29] D. Notbohm, For which pseudo reflection groups are the /?-adic polynomial invariants again a polynomial algebra? Preprint.
Zentralblatt MATH: 0946.14026
[30] D. Notbohm, Spaces with polynomial mod-/? cohomology, Preprint.
Zentralblatt MATH: 0926.55014
[31] G. J. Porter, Higher order Whitehead products, Topology 3 (1965), 123-135.
Zentralblatt MATH: 0149.20204
Mathematical Reviews (MathSciNet): MR174054
[32] L. Saumell, Homotopy commutativity of finite loop spaces, Math. Z. 207 (1991), 319- 334.
Zentralblatt MATH: 0746.55006
Mathematical Reviews (MathSciNet): MR1109669
[33] L. Saumell, Higher homotopy commutativity in localized groups, Math. Z. 219 (1995), 203- 213.
Zentralblatt MATH: 0821.55009
Mathematical Reviews (MathSciNet): MR1337215
[34] M. Slack, A classification theorem for homotopy commutative mod 2 //-spaces with finitely generated cohomology rings, Mem. Amer. Math. Soc. 92 (1991).
Zentralblatt MATH: 0755.55003
Mathematical Reviews (MathSciNet): MR1086565
[35] J. D. Stasheff, Homotopy associativity of /-spaces I, II, Trans. Amer. Math. Soc. 108 (1963), 275-292, 293-312.
Zentralblatt MATH: 0114.39402
Mathematical Reviews (MathSciNet): MR158400
[36] M. Sugawara, On the homotopy commutativity of groups and loop spaces, Mem. College Sci. Univ. Kyoto Ser. A 33 (1960), 257-269.
Zentralblatt MATH: 0113.16903
Mathematical Reviews (MathSciNet): MR120645
[37] H. Toda, On homotopy groups of S3-bundles over spheres, J. Math. Kyoto Univ. 2 (1963), 193-207.
Zentralblatt MATH: 0123.39801
Mathematical Reviews (MathSciNet): MR153014
[38] F. D. Williams, Higher homotopy-commutativity, Trans. Amer. Math. Soc. 139 (1969), 191-206.
Zentralblatt MATH: 0185.27103
Mathematical Reviews (MathSciNet): MR240818
[39] F. D. Williams, Higher Samelson products, J. Pure Appl. Algebra 2 (1972), 249-260
Zentralblatt MATH: 0239.55017
Mathematical Reviews (MathSciNet): MR303533
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