Proceedings of the American Mathematical Society

Author(s): Mingqing Ouyang
Journal: Proc. Amer. Math. Soc. 125 (1997), 1845-1851.
MSC (1991): Primary 57N10; Secondary 57M25
Retrieve article in: PDF
This article is available free of charge

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.

[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

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

Mingqing Ouyang
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: mouyang@math.lsa.umich.edu

DOI: 10.1090/S0002-9939-97-04022-7
PII: S 0002-9939(97)04022-7
Received by editor(s): December 5, 1995
Communicated by: Ronald Stern
Copyright of article: Copyright 1997, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS