On the Schlafli differential formula based on edge lengths of tetrahedron in H 3 and S 3

Yakut, Atakan Tuğkan; Savas, Murat; Kader, Serkan

doi:10.1007/s10711-008-9301-x

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…In the case of the structure group SU(2) ∼ S 3 , the computation of Γ[U] can be reduced to the computation of the volume of a given polyhedron in a space of constant curvature. Discussions on this last problem can be found, for instance, in the articles [31,32,33,34,35,36,37,38].…”

Section: Group Volumementioning

confidence: 99%

Flat connections in three-manifolds and classical Chern–Simons invariant

2017

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A general method for the construction of smooth flat connections on 3-manifolds is introduced. The procedure is strictly connected with the deduction of the fundamental group of a manifold M by means of a Heegaard splitting presentation of M . For any given matrix representation of the fundamental group of M, a corresponding flat connection A on M is specified. It is shown that the associated classical Chern-Simons invariant assumes then a canonical form which is given by the sum of two contributions: the first term is determined by the intersections of the curves in the Heegaard diagram, and the second term is the volume of a region in the representation group which is determined by the representation of π1(M) and by the Heegaard gluing homeomorphism. Examples of flat connections in topologically nontrivial manifolds are presented and the computations of the associated classical Chern-Simons invariants are illustrated

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Section: Group Volumementioning

confidence: 99%

Flat connections in three-manifolds and classical Chern–Simons invariant

2017

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“…The result was generalized to spaces of negative curvature by Sforza (1907) and new proofs given by Kneser (1936). More recent treatments include Milnor (1994), Alekseevskij, Vinberg and Solodovnikov (1993) and Yakut, Savas and Kader (2009).…”

Section: Introductionmentioning

confidence: 98%

Symplectic and semiclassical aspects of the Schläfli identity

Hedeman

Kur

Littlejohn

et al. 2015

J. Phys. A: Math. Theor.

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Abstract. The Schläfli identity, which is important in Regge calculus and loop quantum gravity, is examined from a symplectic and semiclassical standpoint in the special case of flat, 3-dimensional space. In this case a proof is given, based on symplectic geometry. A series of symplectic and Lagrangian manifolds related to the Schläfli identity, including several versions of a Lagrangian manifold of tetrahedra, are discussed. Semiclassical interpretations of the various steps are provided. Possible generalizations to 3-dimensional spaces of constant (nonzero) curvature, involving Poisson-Lie groups and q-deformed spin networks, are discussed.

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“…Yakut, Savas and Kader [YSK09] calculated the Jacobian matrix for a hyperbolic or spherical tetrahedron and represented each entry of the matrix in terms of x ij . The symmetries of the Jacobian matrix are not obvious in their result.…”

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confidence: 99%