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Farrell FT, Jones LE. Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds. Proc Natl Acad Sci U S A. 1986;83(15):5364-6doi: 10.1073/pnas.83.15.5364.
Farrell, F. T., & Jones, L. E. (1986). Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds. Proceedings of the National Academy of Sciences of the United States of America, 83(15), 5364-6. https://doi.org/10.1073/pnas.83.15.5364
Farrell, F T, and Jones, L E. "Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds." Proceedings of the National Academy of Sciences of the United States of America vol. 83,15 (1986): 5364-6. doi: https://doi.org/10.1073/pnas.83.15.5364
Farrell FT, Jones LE. Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds. Proc Natl Acad Sci U S A. 1986 Aug;83(15):5364-6. doi: 10.1073/pnas.83.15.5364. PMID: 16593733; PMCID: PMC386286.
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Proc Natl Acad Sci U S A. 1986 Aug;83(15):5364-6. doi: 10.1073/pnas.83.15.5364.

Algebraic K-theory of spaces stratified fibered over hyperbolic orbifolds.

Proceedings of the National Academy of Sciences of the United States of America

F T Farrell, L E Jones

Affiliations

  1. Department of Mathematics, Columbia University, New York, NY 10027.

PMID: 16593733 PMCID: PMC386286 DOI: 10.1073/pnas.83.15.5364

Abstract

Among other results, we rationally calculate the algebraic K-theory of any discrete cocompact subgroup of a Lie group G, where G is either O(n, 1), U(n, 1), Sp(n, 1), or F(4), in terms of the homology of the double coset space Gamma\G/K, where K is a maximal cocompact subgroup of G. We obtain the formula K(n)(ZGamma) [unk] [unk] congruent with [unk](i=0) (infinity)H(i)(Gamma\G/K; [unk](n-i)), where [unk](j) is a stratified system of Q vector spaces over Gamma\G/K and the vector space [unk](j)(GammagK) corresponding to the double coset GammagK is isomorphic to K(J)(Z(Gamma [unk] gKg(-1))) [unk] Q. Note Gamma [unk] gKg(-1) is a finite subgroup of Gamma. Earlier, a similar formula for discrete cocompact subgroups Gamma of the group of rigid motions of Euclidean space was conjectured by F. T. Farrell and W. C. Hsiang and proven by F. Quinn.

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