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Bordism of manifolds with oriented boundaries


Author: G. E. Mitchell
Journal: Proc. Amer. Math. Soc. 47 (1975), 208-214
DOI: https://doi.org/10.1090/S0002-9939-1975-0350758-0
MathSciNet review: 0350758
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Abstract | References | Additional Information

Abstract: A bordism theory is defined for manifolds with oriented boundaries. The relation of this theory with the ordinary bordism theories is shown. These bordism classes are then characterized via characteristic numbers.


References [Enhancements On Off] (What's this?)

  • [1] M. F. Atiyah, Bordism and cobordism, Proc. Cambridge Philos. Soc. 57 (1961), 200-208. MR 23 #A4150. MR 0126856 (23:A4150)
  • [2] A. Bord La cohomologie $ \bmod 2$ de certains espaces homogènes, Comment. Math. Helv. 27 (1953), 165-197. MR 0057541 (15:244h)
  • [3] R. O. Burdick, Manifolds fibered over the circle, Thesis, University of Virginia, Charlottesville, Va., 1966.
  • [4] P. E. Conner and E. E. Floyd, Differentiable periodic maps, Ergebnisse der Mathematik und ihrer Grenzgebiete, N. F., Band 33, Academic Press, New York; Springer-Verlag, Berlin, 1964. MR 31 #750. MR 0176478 (31:750)
  • [5] -, The relation of cobordism to $ K$-theories, Lecture Notes in Math., no. 28, Springer-Verlag, Berlin and New York, 1966. MR 35 #7344.
  • [6] J. W. Milnor, Differentiable structures on homotopy spheres, Princeton, 1959. (mimeographed notes).
  • [7] -, On the cobordism ring $ {\Omega ^ \ast }$ and a complex analogue. I, Amer. J. Math. 82 (1960), 505-521. MR 22 #9975. MR 0119209 (22:9975)
  • [8] V. A. Rohlin, Intrinsic homologies, Dokl. Akad. Nauk SSSR 89 (1953), 789-792. (Russian) MR 15, 53. MR 0056292 (15:53b)
  • [9] R. E. Stong, Notes on cobordism theory, Princeton Univ. Press, Princeton, N. J., 1968. MR 40 #2108. MR 0248858 (40:2108)
  • [10] R. Thom, Quelques propriétés globales des variétés différentiables, Comment. Math. Helv. 28 (1954), 17-86. MR 15, 890. MR 0061823 (15:890a)
  • [11] C. T. C. Wall, Determination of the cobordism ring, Ann. of Math. (2) 72 (1960), 292-311. MR 22 #11403. MR 0120654 (22:11403)
  • [12] E. H. Spanier, Algebraic topology, McGraw-Hill, New York, 1966. MR 35 #1007. MR 0210112 (35:1007)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0350758-0
Article copyright: © Copyright 1975 American Mathematical Society

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