The cobordism of Real manifolds

• Autorzy: Po Hu
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 55P91: Equivariant homotopy theory
• 55N22: Bordism and cobordism theories, formal group laws

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 1999
• Tom: 161
• Numer: 1-2
• Strony: 119-136

Daty

wydano

1999

otrzymano

1997-10-31

Twórcy

autor

Po Hu

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

Bibliografia

• [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.