Localization of CW-complexes and its applications

Mamoru MIMURA; Goro NISHIDA; Hirosi TODA

doi:10.2969/jmsj/02340593

Mamoru MIMURA, Goro NISHIDA, Hirosi TODA

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1971 Volume 23 Issue 4 Pages 593-624

DOI https://doi.org/10.2969/jmsj/02340593

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Published: 1971 Received: January 28, 1971 Available on J-STAGE: September 29, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 29, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) J. F. Adams, On the non-existence of elements of Hopf-invariant one, Ann. of Math., 72 (1960), 20-104.
2) J. F. Adams, The sphere, considered as an H-space mod p, Quart. J. Math. Oxford (2), 12 (1961), 52-60.
3) D. W. Anderson, Localizing CW-complexes, (mimeographed).
4) M. Arkowitz and C. R. Curjel, The Hurewitz homomorphism and finite homotopy invariants, Trans. Amer. Math. Soc., 110 (1964), 538-551.
5) M. Arkowitz and C. R. Curjel, Zum Begriff des H-Raumes mod _??_, Arch. Math., 16 (1965), 186-190.
6) A. Borel, Sur la cohomologie des espaces fibres principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math., 57 (1953), 115-207.
7) M. Curtis and G. Mislin, Two new H-spaces, Bull. Amer. Math. Soc., 76 (1970), 851-852.
8) P. J. Hilton and J. Roitberg, On principal S³-bundles over spheres, Ann. of Math., 90 (1969), 91-107.
9) I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres, Proc. London Math. Soc. (3), 4 (1954), 196-218.
10) M. Mimura and H. Toda, Cohomology operations and the homotopy of compact Lie groups, I, Topology, 9 (1970), 317-336.
11) M. Mimura and H. Toda, On p-equivalences and p-universal spaces, Comment. Math. Helv., 4 (1971), 87-97.
12) M. Mimura, R. C. O'Neill and H. Toda, On the p-equivalence in the sense of Serre, Japan. J. Math., 40 (1971), 1-10.
13) M. Nakaoka, Cohomology mod p of symmetric products of spheres, J. Inst. Poly. Osaka City Univ., 9 (1958), 1-18.
14) M. Nakaoka, Homology of Γ-products, Sugaku, 10 (1958), 97-104, (Iwanami, in Japanese).
15) R. C. O'Neill, On H-spaces that are CW complexes, Ill. J. Math., 8 (1964), 280-290.
16) H. Samelson, Beiträge zur Topologie der Gruppen-Mannigfaltigkeiten, Ann. of Math., 42 (1941), 1091-1137.
17) J-P. Serre, Groupes d'homotopie et classes des groupes abéliens, Ann. of Math., 58 (1953), 258-294.
18) N. Shimada and T. Yamanoshita, On triviality of the mod p Hopf invariant, Japan. J. Math., 31 (1961), 1-25.
19) E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
20) J. D. Stasheff, Homotopy associativity of H-spaces, I, II, Trans. Amer. Math. Soc., 108 (1963), 275-312.
21) J. D. Stasheff, Manifolds of the homotopy type of (non-Lie) groups, Bull. Amer. Math. Soc., 75 (1969), 998-1000.
22) J. D. Stasheff, H-spaces from a homotopy point of view, Lecture notes in Math., 161 (1970), (Springer).
23) A. Zabrodsky, Homotopy associativity and finite CW-complexes, Topology, 9 (1970), 121-128.

Right : 1) J. F. Adams, On the non-existence of elements of Hopf-invariant one, Ann. of Math., 72 (1960), 20-104.
2) J. F. Adams, The sphere, considered as an H-space mod p, Quart. J. Math. Oxford (2), 12 (1961), 52-60.
3) D. W. Anderson, Localizing CW-complexes, (mimeographed).
4) M. Arkowitz and C. R. Curjel, The Hurewitz homomorphism and finite homotopy invariants, Trans. Amer. Math. Soc., 110 (1964), 538-551.
5) M. Arkowitz and C. R. Curjel, Zum Begriff des H-Raumes mod ℑ, Arch. Math., 16 (1965), 186-190.
6) A. Borel, Sur la cohomologie des espaces fibres principaux et des espaces homogènes de groupes de Lie compacts, Ann. of Math., 57 (1953), 115-207.
7) M. Curtis and G. Mislin, Two new H-spaces, Bull. Amer. Math. Soc., 76 (1970), 851-852.
8) P. J. Hilton and J. Roitberg, On principal S³-bundles over spheres, Ann. of Math., 90 (1969), 91-107.
9) I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres, Proc. London Math. Soc. (3), 4 (1954), 196-218.
10) M. Mimura and H. Toda, Cohomology operations and the homotopy of compact Lie groups, I, Topology, 9 (1970), 317-336.
11) M. Mimura and H. Toda, On p-equivalences and p-universal spaces, Comment. Math. Helv., 4 (1971), 87-97.
12) M. Mimura, R. C. O'Neill and H. Toda, On the p-equivalence in the sense of Serre, Japan. J. Math., 40 (1971), 1-10.
13) M. Nakaoka, Cohomology mod p of symmetric products of spheres, J. Inst. Poly. Osaka City Univ., 9 (1958), 1-18.
14) M. Nakaoka, Homology of Γ-products, Sugaku, 10 (1958), 97-104, (Iwanami, in Japanese).
15) R. C. O'Neill, On H-spaces that are CW complexes, Ill. J. Math., 8 (1964), 280-290.
16) H. Samelson, Beiträge zur Topologie der Gruppen-Mannigfaltigkeiten, Ann. of Math., 42 (1941), 1091-1137.
17) J-P. Serre, Groupes d'homotopie et classes des groupes abéliens, Ann. of Math., 58 (1953), 258-294.
18) N. Shimada and T. Yamanoshita, On triviality of the mod p Hopf invariant, Japan. J. Math., 31 (1961), 1-25.
19) E. H. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966.
20) J. D. Stasheff, Homotopy associativity of H-spaces, I, II, Trans. Amer. Math. Soc., 108 (1963), 275-312.
21) J. D. Stasheff, Manifolds of the homotopy type of (non-Lie) groups, Bull. Amer. Math. Soc., 75 (1969), 998-1000.
22) J. D. Stasheff, H-spaces from a homotopy point of view, Lecture notes in Math., 161 (1970), (Springer).
23) A. Zabrodsky, Homotopy associativity and finite CW-complexes, Topology, 9 (1970), 121-128.

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