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Transactions of the American Mathematical Society

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The $ S\sp{1}$-transfer in surgery theory


Authors: H. J. Munkholm and E. K. Pedersen
Journal: Trans. Amer. Math. Soc. 280 (1983), 277-302
MSC: Primary 57R67; Secondary 18F25
DOI: https://doi.org/10.1090/S0002-9947-1983-0712261-4
MathSciNet review: 712261
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Abstract: Let $ {S^1} \to X \to Y$ be an $ {S^1}$-bundle of Poincaré spaces. If $ f:N \to Y$ is a surgery problem then so is the pullback $ \hat f:M \to X$. We define algebraically a homomorphism $ {\varphi ^!}:{L_n}({\mathbf{Z}}{\pi _1}(Y)) \to {L_{n + 1}}({\mathbf{Z}}{\pi _1}(X))$ and prove that it maps the surgery obstruction for $ f$ to the one for $ \hat f$.


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

  • [1] H. J. Munkholm and E. K. Pedersen, Whitehead transfers for $ {S^1}$-bundles, an algebraic description, Comment. Math. Helv. 56 (1981), 404-430. MR 639359 (83c:57007)
  • [2] E. K. Pedersen, Universal geometric examples for transfer maps in algebraic $ K$- and $ L$-theory, J. Pure Appl. Algebra 22 (1981), 179-192. MR 624571 (82i:57028)

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DOI: https://doi.org/10.1090/S0002-9947-1983-0712261-4
Article copyright: © Copyright 1983 American Mathematical Society

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