Construction and recognition of hyperbolic 3manifolds with geodesic boundary
Authors:
Roberto Frigerio and Carlo Petronio
Journal:
Trans. Amer. Math. Soc. 356 (2004), 32433282
MSC (2000):
Primary 57M50; Secondary 57M25
Published electronically:
August 26, 2003
MathSciNet review:
2052949
Fulltext PDF Free Access
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Abstract: We extend to the context of hyperbolic 3manifolds with geodesic boundary Thurston's approach to hyperbolization by means of geometric triangulations. In particular, we introduce moduli for (partially) truncated hyperbolic tetrahedra, and we discuss consistency and completeness equations. Moreover, building on previous work of Ushijima, we extend Weeks' tilt formula algorithm, which computes the EpsteinPenner canonical decomposition, to an algorithm that computes the Kojima decomposition. Our theory has been exploited to classify all the orientable finitevolume hyperbolic manifolds with nonempty compact geodesic boundary admitting an ideal triangulation with at most four tetrahedra. The theory is particularly interesting in the case of complete finitevolume manifolds with geodesic boundary in which the boundary is noncompact. We include this case using a suitable adjustment of the notion of ideal triangulation, and we show how this case arises within the theory of knots and links.
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Additional Information
Roberto Frigerio
Affiliation:
Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126 Pisa, Italy
Email:
frigerio@sns.it
Carlo Petronio
Affiliation:
Dipartimento di Matematica Applicata, Università di Pisa, Via Bonanno Pisano, 25/B, 6126 Pisa, Italy
Email:
petronio@dma.unipi.it
DOI:
http://dx.doi.org/10.1090/S0002994703033786
PII:
S 00029947(03)033786
Received by editor(s):
December 1, 2001
Received by editor(s) in revised form:
March 20, 2003
Published electronically:
August 26, 2003
Article copyright:
© Copyright 2003
American Mathematical Society
