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Homology tangent bundles and universal bundles


Author: Daniel Henry Gottlieb
Journal: Proc. Amer. Math. Soc. 36 (1972), 246-252
MSC: Primary 57A65
DOI: https://doi.org/10.1090/S0002-9939-1972-0307244-0
MathSciNet review: 0307244
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Abstract: We find results about the evaluation map from the group of homeomorphisms of a closed manifold M and also about fibre bundles where M is the fibre. These facts follow from the observation that the homology tangent bundle is induced from a universal bundle pair.


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  • [1] Guy Allaud, On the classification of fibre spaces, Math. Z. 92 (1966), 110-125. MR 32 #6462. MR 0189035 (32:6462)
  • [2] Armand Borel, Sur la torsion des groupes de Lie, J. Math. Pures Appl. (9) 35 (1956), 127-139. MR 17. 1107. MR 0077871 (17:1107g)
  • [3] -, Topics in the homology theory of fibre bundles, Lecture Notes in Math., no. 36, Springer-Verlag, Berlin and New York, 1967. MR 36 #4559. MR 0221507 (36:4559)
  • [4] Robert F. Brown, On the Lefschetz number and the Euler class, Trans. Amer. Math. Soc. 118 (1965), 174-179. MR 30 #3481. MR 0173268 (30:3481)
  • [5] Albrecht Dold, Halbexakte Homotopiefunktoren, Lecture Notes in Math., no. 12, Springer-Verlag, 1966 (see p. 16.8). MR 33 #6622. MR 0198464 (33:6622)
  • [6] Edward Fadell, Generalized normal bundles for locally-flat imbeddings, Trans. Amer. Math. Soc. 114 (1965), 488-513. MR 31 #4037. MR 0179795 (31:4037)
  • [7] D. H. Gottlieb, On fibre spaces and the evaluation map, Ann. of Math. (2) 87 (1968), 42-55; Corrigendum, ibid. (2) 91 (1970), 640-642. MR 36 #4560; MR 41 #7684. MR 0221508 (36:4560)
  • [8] -, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. MR 0275424 (43:1181)
  • [9] -, Applications of bundle map theory, Trans. Amer. Math. Soc. (to appear). MR 0309111 (46:8222)
  • [10] Edwin H. Spanier, Algebraic topołogy, McGraw-Hill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0307244-0
Keywords: Homology tangent bundle, classifying bundle, Euler class, characteristic classes, topological manifolds, actions
Article copyright: © Copyright 1972 American Mathematical Society

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