The $S^{1}$-transfer in surgery theory
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- by H. J. Munkholm and E. K. Pedersen PDF
- Trans. Amer. Math. Soc. 280 (1983), 277-302 Request permission
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
- Hans J. Munkholm and Erik Kjaer Pedersen, Whitehead transfers for $S^{1}$-bundles, an algebraic description, Comment. Math. Helv. 56 (1981), no. 3, 404–430. MR 639359, DOI 10.1007/BF02566220
- Erik Kjaer Pedersen, Universal geometric examples for transfer maps in algebraic $K$- and $L$-theory, J. Pure Appl. Algebra 22 (1981), no. 2, 179–192. MR 624571, DOI 10.1016/0022-4049(81)90058-X
Additional Information
- © Copyright 1983 American Mathematical Society
- 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