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We present a generalization of Minkowski's classic theorem on the reconstruction of tetrahedra from algebraic data to homogeneously curved spaces.
1970 Quantization and unitary representations
Kostant · 1970
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Kirillov · 1976
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1983 The Yang-Mills equations over riemann surfaces
Atiyah · 1983
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1984 The symplectic nature of fundamental groups of surfaces
Goldman · 1984
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1988 2+1 Dimensional Gravity as an Exactly Soluble System
Witten · 1988
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1992 Three-Dimensional gravity from the Turaev-Viro Invariant
Mizoguchi · 1992
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1992 State Sum Invariants of 3-Manifolds and Quantum 6 j 6j -Symbols
Turaev · 1992
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1994 Extended moduli spaces of flat connections on Riemann surfaces
Jeffrey · 1994
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A Guide to Quantum Groups
Chari · 1995
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1995 Discreteness of Area and Volume in Quantum Gravity
Rovelli · 1995
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The Symplectic Geometry of Polygons in Euclidean Space
Kapovich · 1996
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Lie group valued moment maps
Alekseev · 1998
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1998 Relativistic Spin Networks and Quantum Gravity
Barrett · 1998
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The Quantum Tetrahedron in 3 and 4 Dimensions
Baez · 1999
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Manin pairs and moment maps
Alekseev · 2000
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The Symplectic Geometry of Polygons in Hyperbolic 3-Space
Kapovich · 2000
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2002 Quasi-Poisson manifolds
Alekseev · 2002
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2002 Duistermaat–Heckman measures and moduli spaces of flat bundles over surfaces
Alekseev · 2002
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Treloar · 2002
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2003 Diffeomorphisms and Spin Foam Models
Freidel · 2003
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Alexandrov · 2005
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2006 6 j 6j Symbols for U q ( 𝔰 l 2 ) U_{q}({\mathfrak{s}l}_{2}) and Non-Euclidean Tetrahedra
Taylor · 2006
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2011 4-dimensional spin-foam model with quantum Lorentz group
Han · 2011
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2011 Canonical quantization of non-commutative holonomies in 2+1 loop quantum gravity
Noui · 2011
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2012 Bohr-Sommerfeld Quantization of Space
Bianchi · 2012
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2012 Quantum deformation of two four-dimensional spin foam models
Fairbairn · 2012
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Rovelli · 2007
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2008 LQG Vertex with Finite Immirzi Parameter
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2008 A New Spin Foam Model for 4D Gravity
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2009 Improved and perfect actions in discrete gravity
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2014 Towards the Turaev-Viro amplitudes from a Hamiltonian constraint
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2014 Observables in Loop Quantum Gravity with a cosmological constant
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2014 Deformed Spinor Networks for Loop Gravity: Towards Hyperbolic Twisted Geometries
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Haggard · 2014
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Kabaya · 2014
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2014 Deformation operators of spin networks and coarse-graining
Livine · 2014
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2014 Turaev-Viro amplitudes from 2+1 Loop Quantum Gravity
Pranzetti · 2014
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2015 Closure constraints for hyperbolic tetrahedra
Charles · 2015
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Dittrich · 2015
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