Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on the Chern-Simons invariant
of hyperbolic 3-manifolds

Author: Mingqing Ouyang
Journal: Proc. Amer. Math. Soc. 125 (1997), 1845-1851
MSC (1991): Primary 57N10; Secondary 57M25
MathSciNet review: 1415359
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note we study how the Chern-Simons invariant behaves when two hyperbolic 3-manifolds are glued together along incompressible
thrice-punctured spheres. Such an operation produces many hyperbolic 3-manifolds with different numbers of cusps sharing the same volume and the same Chern-Simons invariant. The results in this note, combined with those of Meyerhoff and Ruberman, give an algorithm for determining the unknown constant in Neumann's simplicial formula for the Chern-Simons invariant of hyperbolic 3-manifolds.

References [Enhancements On Off] (What's this?)

  • [A1] C. Adams, Thrice-punctured spheres in hyperbolic 3-manifolds, Trans. Amer. Math. Soc. 287 (1985), 645-656. MR 86k:57008
  • [A2] C. Adams, Augmented alternating link complements are hyperbolic, London Math. Soc. Lecture Notes 112 (D. B. A. Epstein, ed.), 115-130. MR 89f:57003
  • [M] R. Meyerhoff, Density of the Chern-Simons invariant for hyperbolic 3-manifolds, in Low-dimensional topology and Kleinian groups, London Math. Soc. Lect. Notes 112, D. B. A. Epstein, editor, Cambridge University Press, (1987), 217-240. MR 88k:57033a
  • [MO] R. Meyerhoff and M. Ouyang, The $\eta $-invariant of cusped hyperbolic 3-manifolds, to appear in Canadian Math. Bull.
  • [MR] R. Meyerhoff and D. Ruberman, Mutation and the $\eta $-invariant, J. Differential Geom. 31 (1990), 101-130. MR 91j:57017
  • [N] W. Neumann, Combinatorics of triangulations and the Chern-Simons invariant for hyperbolic 3-manifolds, in Topology'90, Proceedings of the Research Semester on Low Dimensional Topology, de Gruyter Verlag, 1992. MR 93i:57020
  • [Y] T. Yoshida, The $\eta $-invariant of hyperbolic 3-manifolds, Invent. Math. 81 (1985), 473-514. MR 87f:58153

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57N10, 57M25

Retrieve articles in all journals with MSC (1991): 57N10, 57M25

Additional Information

Mingqing Ouyang
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Received by editor(s): December 5, 1995
Communicated by: Ronald Stern
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society