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Algebraic $K$-theory of hyperbolic manifolds

1986
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Bulletin of the American Mathematical Society
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Let r = TT\M where M is a complete hyperbolic manifold with finite volume. We announce (among other results) that Wh T = 0 where Wh T is the Whitehead group of T. We also announce WI12 r = 0, k 0 (ZT) = 0, Kn (ZT) = 0 (for n > 0), and Wh n T 0 Q = 0 (for all n). We calculate the weak homotopy type of the stable topological concordance space C(M), and hence Waldhausen's Wh PL -theory (cf. [22]) of M, in terms of simpler stable concordance spaces. When M is compact, the calculation is in terms of

doi:10.1090/s0273-0979-1986-15412-1
fatcat:idcocepqizccfl2f7jibjwrq2y