Bloch invariants of hyperbolic $3$-manifolds

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Bloch invariants of hyperbolic $3$-manifolds

Walter D. Neumann and Jun Yang

Source: Duke Math. J. Volume 96, Number 1 (1999), 29-59.

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Primary Subjects: 57M27

Secondary Subjects: 19E99, 19F27, 57M50, 57N10, 58J28

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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077228942
Mathematical Reviews number (MathSciNet): MR1663915
Zentralblatt MATH identifier: 0943.57008
Digital Object Identifier: doi:10.1215/S0012-7094-99-09602-3

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References

[1] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. I, Math. Proc. Cambridge Philos. Soc. 77 (1975), 43–69.

Mathematical Reviews (MathSciNet): MR53:1655a

Zentralblatt MATH: 0297.58008

Digital Object Identifier: doi:10.1017/S0305004100049410

[2] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian geometry. II, Math. Proc. Cambridge Philos. Soc. 78 (1975), no. 3, 405–432.

Mathematical Reviews (MathSciNet): MR53:1655b

Zentralblatt MATH: 0314.58016

Digital Object Identifier: doi:10.1017/S0305004100051872

[3] C. Batut, et al., Pari-GP, available from ftp://megrez.ceremab.u-bordeaux.fr/pub/pari/.

[4] A. Beilinson, Higher regulators and values of $L$-functions, J. Soviet Math. 30 (1985), 2036–2070, (English translation).

Mathematical Reviews (MathSciNet): MR760999

[5] S. Bloch, Higher regulators, algebraic $K$-theory, and zeta functions of elliptic curves, lecture notes, Univ. of California, Irvine, 1978.

[6] Armand Borel, Cohomologie de $\rm SL\sbn$ et valeurs de fonctions zeta aux points entiers, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 4 (1977), no. 4, 613–636.

Mathematical Reviews (MathSciNet): MR58:22016

Zentralblatt MATH: 0382.57027

[7] Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1982.

Mathematical Reviews (MathSciNet): MR83k:20002

Zentralblatt MATH: 0584.20036

[8] Shiing-shen Chern and James Simons, Some cohomology classes in principal fiber bundles and their application to riemannian geometry, Proc. Nat. Acad. Sci. U.S.A. 68 (1971), 791–794.

Mathematical Reviews (MathSciNet): MR43:5453

Zentralblatt MATH: 0209.25401

Digital Object Identifier: doi:10.1073/pnas.68.4.791

JSTOR: links.jstor.org

[9] Henri Cohen, A course in computational algebraic number theory, Graduate Texts in Mathematics, vol. 138, Springer-Verlag, Berlin, 1993.

Mathematical Reviews (MathSciNet): MR94i:11105

Zentralblatt MATH: 0786.11071

[10] Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989.

Mathematical Reviews (MathSciNet): MR91b:20001

Zentralblatt MATH: 0665.20001

[11] Johan L. Dupont, Algebra of polytopes and homology of flag complexes, Osaka J. Math. 19 (1982), no. 3, 599–641.

Mathematical Reviews (MathSciNet): MR85f:52014

Zentralblatt MATH: 0499.51014

Project Euclid: euclid.ojm/1200775324

[12] Johan L. Dupont, The dilogarithm as a characteristic class for flat bundles, J. Pure Appl. Algebra 44 (1987), no. 1-3, 137–164, in Proceedings of the Northwestern Conference on Cohomology of Groups (Evanston, Ill., 1985), North-Holland, Amsterdam.

Mathematical Reviews (MathSciNet): MR88k:57032

Zentralblatt MATH: 0624.57024

Digital Object Identifier: doi:10.1016/0022-4049(87)90021-1

[13] J. L. Dupont and F. W. Kamber, Cheeger-Chern-Simons classes of transversally symmetric foliations: dependence relations and eta-invariants, Math. Ann. 295 (1993), no. 3, 449–468.

Mathematical Reviews (MathSciNet): MR95i:57026

Zentralblatt MATH: 0793.57015

Digital Object Identifier: doi:10.1007/BF01444896

[14] Johan L. Dupont and Chih Han Sah, Scissors congruences. II, J. Pure Appl. Algebra 25 (1982), no. 2, 159–195.

Mathematical Reviews (MathSciNet): MR84b:53062b

Zentralblatt MATH: 0496.52004

Digital Object Identifier: doi:10.1016/0022-4049(82)90035-4

[15] D. B. A. Epstein and R. C. Penner, Euclidean decompositions of noncompact hyperbolic manifolds, J. Differential Geom. 27 (1988), no. 1, 67–80.

Mathematical Reviews (MathSciNet): MR89a:57020

Zentralblatt MATH: 0611.53036

Project Euclid: euclid.jdg/1214441650

[16] Henri Gillet, Riemann-Roch theorems for higher algebraic $K$-theory, Adv. in Math. 40 (1981), no. 3, 203–289.

Mathematical Reviews (MathSciNet): MR83m:14013

Zentralblatt MATH: 0478.14010

Digital Object Identifier: doi:10.1016/S0001-8708(81)80006-0

[17] A. B. Goncharov, Volumes of hyperbolic manifolds and mixed Tate motives, Max-Planck-Institut für Mathematik. Bonn, preprint MPI 1996-10, 1996.

[18] O. Goodman, Snap, available from http://www.ms.unimelb.edu.au/~snap.

[19] Benedict H. Gross, On the values of Artin $L$-functions, preprint, Brown University, Providence, 1980.

Mathematical Reviews (MathSciNet): MR2154331

[20] Richard M. Hain, Classical polylogarithms, Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., vol. 55, Amer. Math. Soc., Providence, RI, 1994, pp. 3–42.

Mathematical Reviews (MathSciNet): MR94k:19002

Zentralblatt MATH: 0807.19003

[21] Richard M. Hain and Robert MacPherson, Higher logarithms, Illinois J. Math. 34 (1990), no. 2, 392–475.

Mathematical Reviews (MathSciNet): MR92c:14016

Zentralblatt MATH: 0737.14014

Project Euclid: euclid.ijm/1255988272

[22] A. M. Macbeath, Commensurability of co-compact three-dimensional hyperbolic groups, Duke Math. J. 50 (1983), no. 4, 1245–1253.

Mathematical Reviews (MathSciNet): MR85f:22013

Zentralblatt MATH: 0588.22009

Digital Object Identifier: doi:10.1215/S0012-7094-83-05054-8

Project Euclid: euclid.dmj/1077303499

[23] Robert Meyerhoff, Hyperbolic $3$-manifolds with equal volumes but different Chern-Simons invariants, Low-dimensional topology and Kleinian groups (Coventry/Durham, 1984) ed. D. B. A. Epstein, London Math. Soc. Lecture Note Ser., vol. 112, Cambridge Univ. Press, Cambridge, 1986, pp. 209–215.

Mathematical Reviews (MathSciNet): MR88k:57033b

Zentralblatt MATH: 0622.57009

[24] Robert Meyerhoff and Walter D. Neumann, An asymptotic formula for the eta invariants of hyperbolic $3$-manifolds, Comment. Math. Helv. 67 (1992), no. 1, 28–46.

Mathematical Reviews (MathSciNet): MR92k:57049

Zentralblatt MATH: 0791.57009

Digital Object Identifier: doi:10.1007/BF02566487

[25] John Milnor, Hyperbolic geometry: the first 150 years, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 1, 9–24.

Mathematical Reviews (MathSciNet): MR82m:57005

Zentralblatt MATH: 0486.01006

Digital Object Identifier: doi:10.1090/S0273-0979-1982-14958-8

Project Euclid: euclid.bams/1183548588

[26] John Milnor, On polylogarithms, Hurwitz zeta functions, and the Kubert identities, Enseign. Math. (2) 29 (1983), no. 3-4, 281–322.

Mathematical Reviews (MathSciNet): MR86d:11007

Zentralblatt MATH: 0557.10031

[27] Walter D. Neumann, Combinatorics of triangulations and the Chern-Simons invariant for hyperbolic $3$-manifolds, Topology '90 (Columbus, OH, 1990), Ohio State Univ. Math. Res. Inst. Publ., vol. 1, de Gruyter, Berlin, 1992, pp. 243–271.

Mathematical Reviews (MathSciNet): MR93i:57020

Zentralblatt MATH: 0768.57006

[28] Walter D. Neumann and Alan W. Reid, Amalgamation and the invariant trace field of a Kleinian group, Math. Proc. Cambridge Philos. Soc. 109 (1991), no. 3, 509–515.

Mathematical Reviews (MathSciNet): MR92b:30053

Zentralblatt MATH: 0728.57009

Digital Object Identifier: doi:10.1017/S0305004100069942

[29] Walter D. Neumann and Alan W. Reid, Arithmetic of hyperbolic manifolds, Topology '90 (Columbus, OH, 1990), Ohio State Univ. Math. Res. Inst. Publ., vol. 1, de Gruyter, Berlin, 1992, pp. 273–310.

Mathematical Reviews (MathSciNet): MR94c:57024

Zentralblatt MATH: 0777.57007

[30] Walter D. Neumann and Jun Yang, Invariants from triangulations of hyperbolic $3$-manifolds, Electron. Res. Announc. Amer. Math. Soc. 1 (1995), no. 2, 72–79 (electronic).

Mathematical Reviews (MathSciNet): MR97d:57017

Zentralblatt MATH: 0851.57013

Digital Object Identifier: doi:10.1090/S1079-6762-95-02003-8

[31] Walter D. Neumann and Jun Yang, Rationality problems for $K$-theory and Chern-Simons invariants of hyperbolic $3$-manifolds, Enseign. Math. (2) 41 (1995), no. 3-4, 281–296.

Mathematical Reviews (MathSciNet): MR97h:57038

Zentralblatt MATH: 0861.57022

[32] Walter D. Neumann and Don Zagier, Volumes of hyperbolic three-manifolds, Topology 24 (1985), no. 3, 307–332.

Mathematical Reviews (MathSciNet): MR87j:57008

Zentralblatt MATH: 0589.57015

Digital Object Identifier: doi:10.1016/0040-9383(85)90004-7

[33] Mingqing Ouyang, A simplicial formula for the $\eta$-invariant of hyperbolic $3$-manifolds, Topology 36 (1997), no. 2, 411–421.

Mathematical Reviews (MathSciNet): MR97i:57013

Zentralblatt MATH: 0871.57012

Digital Object Identifier: doi:10.1016/0040-9383(96)00013-4

[34] Dinakar Ramakrishnan, Regulators, algebraic cycles, and values of $L$-functions, Algebraic $K$-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math., vol. 83, Amer. Math. Soc., Providence, RI, 1989, pp. 183–310.

Mathematical Reviews (MathSciNet): MR90e:11094

Zentralblatt MATH: 0694.14002

[35] M. Rapoport, Comparison of the regulators of Beĭlinson and of Borel, Beĭlinson's conjectures on special values of $L$-functions ed. M. Rapoport, et al., Perspect. Math., vol. 4, Academic Press, Boston, MA, 1988, pp. 169–192.

Mathematical Reviews (MathSciNet): MR89j:11114

Zentralblatt MATH: 0667.14005

[36] Alan W. Reid, A note on trace-fields of Kleinian groups, Bull. London Math. Soc. 22 (1990), no. 4, 349–352.

Mathematical Reviews (MathSciNet): MR91d:20056

Zentralblatt MATH: 0706.20038

Digital Object Identifier: doi:10.1112/blms/22.4.349

[37] Chih Han Sah, Scissors congruences. I. The Gauss-Bonnet map, Math. Scand. 49 (1981), no. 2, 181–210 (1982).

Mathematical Reviews (MathSciNet): MR84b:53062a

Zentralblatt MATH: 0496.52003

[38] A. A. Suslin, Algebraic $K$-theory of fields, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), vol. I, Amer. Math. Soc., Providence, 1987, pp. 222–244.

Zentralblatt MATH: 0675.12005

Mathematical Reviews (MathSciNet): MR934225

[39] A. A. Suslin, $K\sb 3$ of a field, and the Bloch group, Trudy Mat. Inst. Steklov. 183 (1990), 180–199, 229, (in Russian), English translation in Proc. Steklov Inst. Math. 183, no. 4 (1991), 217–239.

Mathematical Reviews (MathSciNet): MR91k:19003

Zentralblatt MATH: 0741.19005

[40] W. P. Thurston, The geometry and topology of $3$-manifolds, lecture notes, Princeton University, Princeton, 1977.

[41] William P. Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), no. 3, 357–381.

Mathematical Reviews (MathSciNet): MR83h:57019

Zentralblatt MATH: 0496.57005

Digital Object Identifier: doi:10.1090/S0273-0979-1982-15003-0

Project Euclid: euclid.bams/1183548782

[42] William P. Thurston, Hyperbolic structures on $3$-manifolds. I. Deformation of acylindrical manifolds, Ann. of Math. (2) 124 (1986), no. 2, 203–246.

Mathematical Reviews (MathSciNet): MR88g:57014

Zentralblatt MATH: 0668.57015

Digital Object Identifier: doi:10.2307/1971277

JSTOR: links.jstor.org

[43] J. Weeks, Snappea, available from ftp://geom.umn.edu/pub/software/snappea/.

[44] Tomoyoshi Yoshida, The $\eta$-invariant of hyperbolic $3$-manifolds, Invent. Math. 81 (1985), no. 3, 473–514.

Mathematical Reviews (MathSciNet): MR87f:58153

Zentralblatt MATH: 0594.58012

Digital Object Identifier: doi:10.1007/BF01388583

[45] Don Zagier, The Bloch-Wigner-Ramakrishnan polylogarithm function, Math. Ann. 286 (1990), no. 1-3, 613–624.

Mathematical Reviews (MathSciNet): MR90k:11153

Zentralblatt MATH: 0698.33001

Digital Object Identifier: doi:10.1007/BF01453591

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