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Geometrical construction of holonomy in three-dimensional hyperbolic manifold

Y Fujiwara

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In (2+1)-dimensional gravity without matter, a spacetime is represented by a (pseudo-) Riemannian manifold of constant curvature. Though locally trivial, it can have a rich geometric structure, which is completely described by holonomy. The authors extracts an invariant of geometric structure out of holonomy. The author also shows an explicit construction of holonomy for hyperbolic manifolds which represent quantum nucleation of the universe in (2+1)-dimensional gravity.


PACS

02.40.-k Geometry, differential geometry, and topology

04.60.-m Quantum gravity

MSC

83Cxx General relativity

Subjects

Mathematical physics

Gravitation and cosmology

Dates

Issue 2 (February 1993)



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