Geodesic
Invariants from triangulations of hyperbolic 3-manifolds
Neumann, Walter1 ; Yang, Jun2
1 Department of Mathematics The University of Melbourne Carlton, Vic 3052 Australia
2 Department of Mathematics Duke University Durham NC 27707
Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 2, pp. 72-79.

Voir la notice de l'article provenant de la source American Mathematical Society

For any finite volume hyperbolic 3-manifold $M$ we use ideal triangulation to define an invariant $\beta (M)$ in the Bloch group $\mathcal {B}(\mathbb {C})$. It actually lies in the subgroup of $\mathcal {B}(\mathbb {C})$ determined by the invariant trace field of $M$. The Chern-Simons invariant of $M$ is determined modulo rationals by $\beta (M)$. This implies rationality and — assuming the Ramakrishnan conjecture — irrationality results for Chern Simons invariants.
DOI : 10.1090/S1079-6762-95-02003-8

Neumann, Walter 1 ; Yang, Jun 2

1 Department of Mathematics The University of Melbourne Carlton, Vic 3052 Australia
2 Department of Mathematics Duke University Durham NC 27707 
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Neumann, Walter; Yang, Jun. Invariants from triangulations of hyperbolic 3-manifolds. Electronic research announcements of the American Mathematical Society, Tome 01 (1995) no. 2, pp. 72-79. doi : 10.1090/S1079-6762-95-02003-8. http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-95-02003-8/

[1] Borel, Armand Cohomologie de 𝑆𝐿_{𝑛} et valeurs de fonctions zeta aux points entiers Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 1977 613 636

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

[3] Dicks, Warren, Dunwoody, M. J. Groups acting on graphs 1989

[4] Dupont, Johan L. The dilogarithm as a characteristic class for flat bundles J. Pure Appl. Algebra 1987 137 164

[5] Sah, Chih Han Scissors congruences. I. The Gauss-Bonnet map Math. Scand. 1981

[6] Epstein, D. B. A., Penner, R. C. Euclidean decompositions of noncompact hyperbolic manifolds J. Differential Geom. 1988 67 80

[7] Hain, Richard M. Classical polylogarithms 1994 3 42

[8] Meyerhoff, Robert Density of the Chern-Simons invariant for hyperbolic 3-manifolds 1986 217 239

[9] Neumann, Walter D. Combinatorics of triangulations and the Chern-Simons invariant for hyperbolic 3-manifolds 1992 243 271

[10] Neumann, Walter D., Reid, Alan W. Arithmetic of hyperbolic manifolds 1992 273 310

[11] Neumann, Walter D., Reid, Alan W. Amalgamation and the invariant trace field of a Kleinian group Math. Proc. Cambridge Philos. Soc. 1991 509 515

[12] Neumann, Walter D., Zagier, Don Volumes of hyperbolic three-manifolds Topology 1985 307 332

[13] Ramakrishnan, Dinakar Regulators, algebraic cycles, and values of 𝐿-functions 1989 183 310

[14] Reid, Alan W. A note on trace-fields of Kleinian groups Bull. London Math. Soc. 1990 349 352

[15] Suslin, A. A. Algebraic 𝐾-theory of fields 1987 222 244

[16] Thurston, William P. Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds Ann. of Math. (2) 1986 203 246

[17] Thurston, William P. Three-dimensional manifolds, Kleinian groups and hyperbolic geometry Bull. Amer. Math. Soc. (N.S.) 1982 357 381

[18] Zagier, Don Polylogarithms, Dedekind zeta functions and the algebraic 𝐾-theory of fields 1991 391 430

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