ArticleOriginal scientific text

Title

The cobordism of Real manifolds

Authors 1

Affiliations

  1. Department of Mathematics, University of Chicago, 5734 South University Avenue, Chicago, IL 60637, U.S.A.

Abstract

We calculate completely the Real cobordism groups, introduced by Landweber and Fujii, in terms of homotopy groups of known spectra.

Bibliography

  1. S. Araki, Orientations in τ-cohomology theories, Japan J. Math. 5 (1979), 403-430.
  2. S. Araki and K. Iriye, Equivariant stable homotopy groups of spheres with involutions, I, Osaka J. Math. 19 (1982), 1-55.
  3. S. Araki and M. Murayama, τ-cohomology theories, Japan J. Math. 4 (1978), 363-416.
  4. M. F. Atiyah, K-theory and Reality, Quart. J. Math. Oxford (2) 17 (1966), 367-386.
  5. M. F. Atiyah, R. Bott and A. Shapiro, Clifford modules, Topology 3 (1964), suppl. 1, 3-38.
  6. M. F. Atiyah and G. B. Segal, Equivariant K-theory and completion, J. Differential Geom. 3 (1969) 1-18.
  7. P. E. Conner and E. E. Floyd, Differentiable Periodic Maps, Academic Press, New York, 1964.
  8. S. R. Costenoble and S. Waner, G-transversality revisited, Proc. Amer. Math. Soc. 116 (1992), 535-546.
  9. T. tom Dieck, Bordisms of G-manifolds and integrality theorems, Topology 9 (1970), 345-358.
  10. M. Fujii, Cobordism theory with reality, Math. J. Okayama Univ. 18 (1976), 171-188.
  11. M. Fujii, On the relation of real cobordism to KR-theory, ibid. 19 (1977), 147-158.
  12. M. Fujii, Bordism theory with reality and duality theorem of Poincaré type, ibid. 30 (1988), 151-160.
  13. I. Kriz, A Real analogue of the Adams-Novikov spectral sequence, in preparation.
  14. P. S. Landweber, Fixed point free conjugations on complex manifolds, Ann. of Math. (2) 86 (1967), 491-502.
  15. P. S. Landweber, Conjugations on complex manifolds and equivariant homotopy of MU, Bull. Amer. Math. Soc. 74 (1968), 271-274.
  16. L. G. Lewis, J. P. May and M. Steinberger, Equivariant Stable Homotopy Theory, with contributions by J. E. McClure, Lecture Notes in Math. 1213, Springer, Berlin, 1986.
  17. J. Milnor, Differentiable Topology, Princeton Univ. Press, 1958.
  18. J. Milnor and J. W. Stasheff, Characteristic Classes, Princeton Univ. Press and Univ. of Tokyo Press, 1974.
  19. R. E. Stong, Notes on Cobordism Theory, Princeton Univ. Press, 1968.
  20. A. G. Wasserman, Equivariant differential topology, Topology 8 (1969), 127-150.
Pages:
119-136
Main language of publication
English
Received
1997-10-31
Published
1999
Exact and natural sciences