Minimal crystallizations of 3-manifolds with boundary

Basak, Biplab; Binjola, Manisha

doi:10.48550/arxiv.2001.10214

Cited by 1 publication

(3 citation statements)

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“…Remark 5.9. A similar result has recently been proven in [94] using a completely different approach by applying techniques from crystallization theory. More precisely, it was shown that…”

Section: Smallest Matching Graphs and Gurau Degreesupporting

confidence: 74%

“…The graph on the left-hand side can also be found as a special case in Example 11 of[94]. However, they authors of this paper give no geometric construction of the corresponding complex, but rather argue that it has to represent the solid torus by its properties.…”

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confidence: 99%

“…11 A closer analysis reveals that the graphs G 4,5,6 indeed represent solid tori too, e.g. by using Theorem 14 of[94], which tells us that every core graph representing a manifold with boundary γ and with strictly less than 14 internal vertices represents the solid torus.…”

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confidence: 99%

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Transition Amplitudes in 3D Quantum Gravity: Boundaries and Holography in the Coloured Boulatov Model

Goeller¹,

Oriti²,

Schmid³

2022

Preprint

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We consider transition amplitudes in the coloured simplicial Boulatov model for three-dimensional Riemannian quantum gravity. First, we discuss aspects of the topology of coloured graphs with non-empty boundaries. Using a modification of the standard rooting procedure of coloured tensor models, we then write transition amplitudes systematically as topological expansions. We analyse the transition amplitudes for the simplest boundary topology, the 2-sphere, and prove that they factorize into a sum entirely given by the combinatorics of the boundary spin network state and that the leading order is given by graphs representing the closed 3-ball in the large N limit. This is the first step towards a more detailed study of the holographic nature of coloured Boulatov-type GFT models for topological field theories and quantum gravity. Contents

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“…Remark 5.9. A similar result has recently been proven in [94] using a completely different approach by applying techniques from crystallization theory. More precisely, it was shown that…”

Section: Smallest Matching Graphs and Gurau Degreesupporting

confidence: 74%

mentioning

confidence: 99%