G-degree for singular manifolds

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.

14 pages, 1 figure; improvements suggested by referees. Published online 24 October 2017 in RACSAM

References in corpus (5)

• Colored Tensor Models - a Review
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Topology in colored tensor models via crystallization theory
• 4-colored graphs and knot/link complements
• Compact 3-manifolds via 4-colored graphs

Cited by in corpus (9)

• Topology in colored tensor models via crystallization theory
• Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity
• Combinatorial properties of the G-degree
• Kirby diagrams and 5-colored graphs representing compact 4-manifolds
• Classifying compact 4-manifolds via generalized regular genus and G-degree
• Regular genus and gem-complexity of some mapping tori
• Crystallizations of compact 4-manifolds minimizing combinatorially defined PL-invariants
• Compact n-manifolds via (n+1)-colored graphs: a new approach
• Trisections of PL 4-manifolds arising from colored triangulations