Comment on `Lost in Translation: Topological Singularities in Group Field Theory'

TL;DR

This paper challenges Gurau's claim by demonstrating that the gluing spaces in 3D group field theory are genuine pseudo-manifolds despite not being properly triangulated, with singularities of codimension at least two.

Contribution

The paper provides a counterargument showing that these spaces are true pseudo-manifolds, refining the understanding of their topological structure.

Findings

Gluing spaces are genuine pseudo-manifolds

Singular locus has codimension at least two

Counteracts Gurau's previous claim

Abstract

Gurau argued in [arXiv:1006.0714] that the gluing spaces arising as Feynman diagrams of three-dimensional group field theory are not all pseudo-manifolds. I dispute this conclusion: albeit not properly triangulated, these spaces are genuine pseudo-manifolds, viz. their singular locus is of codimension at least two.