Trisections in colored tensor models

TL;DR

This paper introduces a method to construct (quasi-)trisection diagrams for closed (pseudo-)manifolds derived from colored tensor models, broadening the scope beyond previous crystallization-based approaches.

Contribution

It generalizes the construction of trisection diagrams to a wider class of manifolds generated by colored tensor models, without restrictions on the triangulation size.

Findings

Constructed (quasi-)trisection diagrams for a broad class of manifolds

Extended previous methods to include pseudo-manifolds

Speculated on further generalizations for other tensor model-generated spaces

Abstract

We give a procedure to construct (quasi-)trisection diagrams for closed (pseudo-)manifolds generated by colored tensor models without restrictions on the number of simplices in the triangulation, therefore generalizing previous works in the context of crystallizations and PL-manifolds. We further speculate on generalization of similar constructions for a class of pseudo-manifolds generated by simplicial colored tensor models.