Surgery up to homotopy equivalence for nonpositively curved manifolds
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- by A. Nicas and C. Stark PDF
- Proc. Amer. Math. Soc. 91 (1984), 323-325 Request permission
Abstract:
Let ${M^n}$ be a smooth closed manifold which admits a metric of nonpositive curvature. We show, using a theorem of Farrell and Hsiang, that if $n + k \geqslant 6$, then the surgery obstruction map $\left [ {M \times {D^k},\partial ;G / {\text {TOP}}} \right ] \to L_{n + k}^h\left ( {{\pi _1}M,{w_1}\left ( M \right )} \right )$ is injective, where $L_ * ^h$ are the obstruction groups for surgery up to homotopy equivalence.References
- F. T. Farrell and W. C. Hsiang, On Novikov’s conjecture for nonpositively curved manifolds. I, Ann. of Math. (2) 113 (1981), no. 1, 199–209. MR 604047, DOI 10.2307/1971138
- Robion C. Kirby and Laurence C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Annals of Mathematics Studies, No. 88, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1977. With notes by John Milnor and Michael Atiyah. MR 0645390
- Kyung Whan Kwun and R. H. Szczarba, Product and sum theorems for Whitehead torsion, Ann. of Math. (2) 82 (1965), 183–190. MR 182972, DOI 10.2307/1970568
- Andrew J. Nicas, Induction theorems for groups of homotopy manifold structures, Mem. Amer. Math. Soc. 39 (1982), no. 267, vi+108. MR 668807, DOI 10.1090/memo/0267
- C. T. C. Wall, Surgery on compact manifolds, London Mathematical Society Monographs, No. 1, Academic Press, London-New York, 1970. MR 0431216
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 323-325
- MSC: Primary 57R67; Secondary 57R65
- DOI: https://doi.org/10.1090/S0002-9939-1984-0740195-4
- MathSciNet review: 740195