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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Surgery up to homotopy equivalence for nonpositively curved manifolds


Authors: A. Nicas and C. Stark
Journal: Proc. Amer. Math. Soc. 91 (1984), 323-325
MSC: Primary 57R67; Secondary 57R65
MathSciNet review: 740195
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1984-0740195-4
PII: S 0002-9939(1984)0740195-4
Article copyright: © Copyright 1984 American Mathematical Society