Abstract
It is the purpose of this paper to prove that there is a decresing filtration of complex cobordism theory U*(−) consisting of Z2-graded cohomology theories such that the associated quotients are determined by the complex K-theory K*(−).
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Literatur
ATIYAH, M.F.: Vector bundles and the Künneth formula. Topology1, 245–248 (1962).
CONNER, P.E., FLOYD, E.E.: Differential periodic maps. Springer 1964.
CONNER, P.e., FLOYD, E.E.: The relation of cobordism to K-theories. Lecture Notes in Mathematics28. Springer 1966.
CONNER, P.E., SMITH, L.: On the complex bordism of finite complexes. Inst. haut. Étud. sci., Publ. math.37, 117–221 (1969).
DYER, E.: Cohomology theories. New York: Benjamin 1969.
HIRZEBRUCH, F.: Topological methods of algebraic geometry. Springer 1966.
LANDWEBER, P.S.: Künneth formulas for bordism theories. Trans. Am. Math. Soc.121, 242–256 (1966).
MILNOR, J.W.: On the cobordism ring Ω* and a complex analogue. Amer. J. Math.82, 505–521 (1960).
NOVIKOV, S.P.: Homotopieeigenschaften von Thom-Komplexen. Mat. Sb. (N.S.)57, 407–442 (1962). (Russisch).
SMITH, L.: On the finite generation of Ω U* (X). J. Math. Mech.18, 1017–1024 (1969).
SMITH, L.: Lectures on the complex bordism of finite complexes. Applications. Proc. Adv. Study Inst. Alg. Top., Aarhus 1970.
STONG, R. E.: Notes on cobordism theory. Princeton University Press 1968.
WHITEHEAD, G.W.: Generalized homology theories. Trans. Am. Math. Soc.102, 227–283 (1962).
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Wolff, G. Der Einfluss von K*(−) auf U*(−). Manuscripta Math 10, 141–161 (1973). https://doi.org/10.1007/BF01475039
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DOI: https://doi.org/10.1007/BF01475039