On odd dimensional surgery with finite fundamental group
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- by Jean-Claude Hausmann PDF
- Proc. Amer. Math. Soc. 62 (1977), 199-205 Request permission
Abstract:
One proves that, for any finite group G and homomorphism $\omega :G \to {\mathbf {Z}}/2{\mathbf {Z}}$, the natural homomorphism $L_{2k + 1}^h({\mathbf {Z}}G,\omega ) \to L_{2k + 1}^h({\mathbf {Q}}G,\omega )$ between Wall surgery groups is identically zero. Some results concerning the exponent of $L_{2k + 1}^h({\mathbf {Z}}G;\omega )$ are deduced.References
- Anthony Bak, Odd dimension surgery groups of odd torsion groups vanish, Topology 14 (1975), no. 4, 367–374. MR 400263, DOI 10.1016/0040-9383(75)90021-X —, The computation of surgery groups of finite groups with abelian 2-hyperelementary, Algebraic K-theory, Lecture Notes in Math., Springer, Berlin and New York, vol. 551, pp. 384-409.
- Hyman Bass, Unitary algebraic $K$-theory, Algebraic $K$-theory, III: Hermitian $K$-theory and geometric applications (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972) Lecture Notes in Math., Vol. 343, Springer, Berlin, 1973, pp. 57–265. MR 0371994
- Sylvain E. Cappell and Julius L. Shaneson, The codimension two placement problem and homology equivalent manifolds, Ann. of Math. (2) 99 (1974), 277–348. MR 339216, DOI 10.2307/1970901
- Francis X. Connolly, Linking numbers and surgery, Topology 12 (1973), 389–409. MR 334245, DOI 10.1016/0040-9383(73)90031-1
- Andreas W. M. Dress, Induction and structure theorems for orthogonal representations of finite groups, Ann. of Math. (2) 102 (1975), no. 2, 291–325. MR 387392, DOI 10.2307/1971033 R. M. Geist, Semicharacteristic detection of obstructions to rational homotopy equivalence, Notices Amer. Math. Soc. 21 (1974), A-451. Abstract #74T-G72.
- Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
- Michel A. Kervaire and John W. Milnor, Groups of homotopy spheres. I, Ann. of Math. (2) 77 (1963), 504–537. MR 148075, DOI 10.1090/S0273-0979-2015-01504-1
- William Pardon, Local surgery and applications to the theory of quadratic forms, Bull. Amer. Math. Soc. 82 (1976), no. 1, 131–133. MR 397751, DOI 10.1090/S0002-9904-1976-13992-4
- William Pardon, The exact sequence of a localization for Witt groups, Algebraic $K$-theory (Proc. Conf., Northwestern Univ., Evanston, Ill., 1976) Lecture Notes in Math., Vol. 551, Springer, Berlin, 1976, pp. 336–379. MR 0486068
- D. S. Passman and Ted Petrie, Surgery with coefficients in a field, Ann. of Math. (2) 95 (1972), 385–405. MR 310913, DOI 10.2307/1970866
- C. T. C. Wall, Surgery of non-simply-connected manifolds, Ann. of Math. (2) 84 (1966), 217–276. MR 212827, DOI 10.2307/1970519
- C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216
- C. T. C. Wall, Classification of Hermitian Forms. VI. Group rings, Ann. of Math. (2) 103 (1976), no. 1, 1–80. MR 432737, DOI 10.2307/1971019
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 62 (1977), 199-205
- MSC: Primary 57D65
- DOI: https://doi.org/10.1090/S0002-9939-1977-0433473-6
- MathSciNet review: 0433473