Duke Mathematical Journal

On the torsion in $K_4(\mathbb{Z})$ and $K_5(\mathbb{Z})$

Ronnie Lee and R. H. Szczarba
Source: Duke Math. J. Volume 45, Number 1 (1978), 101-129.
First Page: Show Hide
Primary Subjects: 18F25
Secondary Subjects: 10E45, 55F40
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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077312690
Mathematical Reviews number (MathSciNet): MR0491894
Zentralblatt MATH identifier: 0385.18009
Digital Object Identifier: doi:10.1215/S0012-7094-78-04508-8

References

[1] H. Bass, $K$-theory and stable algebra, Inst. Hautes Études Sci. Publ. Math. (1964), no. 22, 5–60.
Mathematical Reviews (MathSciNet): MR30:4805
Digital Object Identifier: doi:10.1007/BF02684689
[2] A. Borel, Seminar on transformation groups, With contributions by G. Bredon, E. E. Floyd, D. Montgomery, R. Palais. Annals of Mathematics Studies, No. 46, Princeton University Press, Princeton, N.J., 1960.
Mathematical Reviews (MathSciNet): MR22:7129
Zentralblatt MATH: 0091.37202
[3] A. Borel, Stable real cohomology of arithmetic groups, Ann. Sci. École Norm. Sup. (4) 7 (1974), 235–272 (1975).
Mathematical Reviews (MathSciNet): MR52:8338
Zentralblatt MATH: 0316.57026
[4] A. Borel and J.-P. Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973), 436–491.
Mathematical Reviews (MathSciNet): MR52:8337
Zentralblatt MATH: 0274.22011
Digital Object Identifier: doi:10.1007/BF02566134
[5] N. Bourbaki, Éléments de mathématique. Fasc. XXXVII. Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie libres. Chapitre III: Groupes de Lie, Hermann, Paris, 1972.
Mathematical Reviews (MathSciNet): MR58:28083a
Zentralblatt MATH: 0244.22007
[6] G. Bredon, Sheaf theory, McGraw-Hill Book Co., New York, 1967.
Mathematical Reviews (MathSciNet): MR36:4552
[7] K. Brown, High dimensional cohomology of discrete groups, to appear in Proc. Nat. Acad. Sci. U.S.A.
Mathematical Reviews (MathSciNet): MR419682
Zentralblatt MATH: 0339.20013
Digital Object Identifier: doi:10.1073/pnas.73.6.1795
[8] M. Karoubi, Périodicité de la $K$-théorie hermitienne, Algebraic $K$-theory, III: Hermitian $K$-theory and geometric applications (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 301–411. Lecture Notes in Math., Vol. 343.
Mathematical Reviews (MathSciNet): MR52:3284
Zentralblatt MATH: 0274.18016
[9] R. Lee and R. H. Szczarba, On the homology of congruence subgroups and $K\sb{3}({\bf Z})$, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), 651–653.
Mathematical Reviews (MathSciNet): MR52:5825
Zentralblatt MATH: 0305.18008
Digital Object Identifier: doi:10.1073/pnas.72.2.651
[10] R. Lee and R. H. Szczarba, On the homology and cohomology of congruence subgroups, Invent. Math. 33 (1976), no. 1, 15–53.
Mathematical Reviews (MathSciNet): MR54:10485
Zentralblatt MATH: 0332.18015
Digital Object Identifier: doi:10.1007/BF01425503
[11] R. Lee and R. H. Szczarba, The group $K\sb{3}(Z)$ is cyclic of order forty-eight, Ann. of Math. (2) 104 (1976), no. 1, 31–60.
Mathematical Reviews (MathSciNet): MR56:1309
Zentralblatt MATH: 0341.18008
Digital Object Identifier: doi:10.2307/1971055
[12] J. Milnor, Introduction to algebraic $K$-theory, Princeton University Press, Princeton, N.J., 1971.
Mathematical Reviews (MathSciNet): MR50:2304
Zentralblatt MATH: 0237.18005
[13] A. Ash, D. Mumford, M. Rapoport, and Y. Tai, Smooth compactification of locally symmetric varieties, Math. Sci. Press, Brookline, Mass., 1975.
Mathematical Reviews (MathSciNet): MR56:15642
Zentralblatt MATH: 0334.14007
[14] D. Quillen, Higher algebraic $K$-theory. I, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 85–147. Lecture Notes in Math., Vol. 341.
Mathematical Reviews (MathSciNet): MR49:2895
Zentralblatt MATH: 0292.18004
[15] D. Quillen, Finite generation of the groups $K\sb{i}$ of rings of algebraic integers, Algebraic $K$-theory, I: Higher $K$-theories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 179–198. Lecture Notes in Math., Vol. 341.
Mathematical Reviews (MathSciNet): MR50:2305
Zentralblatt MATH: 0355.18018
[16] D. Quillen, On the cohomology and $K$-theory of the general linear groups over a finite field, Ann. of Math. (2) 96 (1972), 552–586.
Mathematical Reviews (MathSciNet): MR47:3565
Zentralblatt MATH: 0249.18022
Digital Object Identifier: doi:10.2307/1970825
[17] C. Soulé, Cohomologie de $SL_3(\mathbb{Z})$, preprint.
[18] G. Voronoi, Nouvelle applications des paramètres continus à la théorie des formes quadratiques I, Crelle 133 (1907), 97–178.
[19] C. Soulé, Addendum to the article: “On the torsion in $K\sb\ast ({\bf Z})$”, Duke Math. J. 45 (1978), no. 1, 131–132.
Mathematical Reviews (MathSciNet): MR58:11074b
Zentralblatt MATH: 0385.18010
Digital Object Identifier: doi:10.1215/S0012-7094-78-04509-X
Project Euclid: euclid.dmj/1077312691
[20] E. S. Barnes, The complete enumeration of extreme senary forms, Philos. Trans. Roy. Soc. London. Ser. A. 249 (1957), 461–506.
Mathematical Reviews (MathSciNet): MR19,251d
Zentralblatt MATH: 0077.26601
Digital Object Identifier: doi:10.1098/rsta.1957.0005
[21] S. Lichtenbaum, Values of zeta-functions, étale cohomology, and algebraic $K$-theory, Algebraic $K$-theory, II: “Classical” algebraic $K$-theory and connections with arithmetic (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Springer, Berlin, 1973, 489–501. Lecture Notes in Math., Vol. 342.
Mathematical Reviews (MathSciNet): MR53:10765
Zentralblatt MATH: 0284.12005

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