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G-degree for singular manifolds
Geometric Topology · Submitted 22 Jun 2017
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In particular, the complete topological classification up to G-degree 6 is obtained in dimension 3, where all 4-colored graphs represent singular manifolds.
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The abstract, sentence by sentence
The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). In particular, the complete topological classification up to G-degree 6 is obtained in dimension 3, where all 4-colored graphs represent singular manifolds.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. | background 1.00 | 0.05 | 0.03 | asserted 1.00 |
| s1 | The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). | contribution 1.00 | 0.85 | 0.10 | asserted 0.98 |
| s2 | In particular, the complete topological classification up to G-degree 6 is obtained in dimension 3, where all 4-colored graphs represent singular manifolds. | result 0.98 | 0.92 | 0.69 | asserted 1.00 |
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The paper
Original abstract
The G-degree of colored graphs is a key concept in the approach to Quantum Gravity via tensor models. The present paper studies the properties of the G-degree for the large class of graphs representing singular manifolds (including closed PL manifolds). In particular, the complete topological classification up to G-degree 6 is obtained in dimension 3, where all 4-colored graphs represent singular manifolds.
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How the literature uses it
1 arXiv paper cite this in 2 sentences
Papers citing it
Cites it as background 1 paper
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Des publications récentes explorent les propriétés topologiques du degré introduit par Gurau dans le contexte des modèles de tenseurs aléatoires colorés [ref] .
Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity · Introduction · 0.97
What it cites · 6 sentences without a confident label
Compares with 1 paper
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Statements (a) and (b) of the above theorem improve, for $d≥4$ and within the set $G_d+1^(s)$, the results of [ref] and [ref] respectively.
Topology in colored tensor models via crystallization theory · General properties of the G-degree · 0.98
Cites as support 1 paper
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Statement (b) follows from statement (a), by recalling that, if $Γ$ is a bipartite $(d+1)$-colored graph such that $ω_G(Γ) < d!/2$, then $|K(Γ)|≅_PL𝕊^d$ ( [ref] ).
Topology in colored tensor models via crystallization theory · General properties of the G-degree · 0.99
Cites as background 1 paper
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We now sketch the rôle played by the G-degree in the 1/N expansion within colored tensor models theory: a more detailed description of these relationships between Quantum Gravity, tensor models and topology of colored graphs may be found in [ref] , [ref] , [ref] , [ref] .
Topology in colored tensor models via crystallization theory · The physical meaning of the G-degree · 0.98
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