Topological Graph Polynomials in Colored Group Field Theory

TL;DR

This paper extends topological graph polynomials to Colored Group Field Theory graphs, providing a new algebraic framework for analyzing their topological properties in arbitrary dimensions.

Contribution

It introduces a generalized topological polynomial for Colored Group Field Theory graphs, expanding the mathematical tools available for their topological analysis.

Findings

Defined the boundary graph as a cellular complex.

Generalized Tutte polynomials to Colored Group Field Theory graphs.

Established a new algebraic framework for topological analysis.

Abstract

In this paper we analyze the open Feynman graphs of the Colored Group Field Theory introduced in [arXiv:0907.2582]. We define the boundary graph $\cG_{\partial}$ of an open graph $\cG$ and prove it is a cellular complex. Using this structure we generalize the topological (Bollobas-Riordan) Tutte polynomials associated to (ribbon) graphs to topological polynomials adapted to Colored Group Field Theory graphs in arbitrary dimension.