Graded spherical skein 2+1-G-HQFT and modified Turaev-Viro invariants

TL;DR

This paper develops a G-graded extension of skein modules and chromatic maps to construct a 2+1-dimensional G-HQFT, connecting quantum group representations at roots of unity with modified Turaev-Viro invariants.

Contribution

It introduces a G-graded framework for skein modules and chromatic maps, enabling the construction of a new 2+1-G-HQFT from quantum group representations.

Findings

Constructed a G-graded chromatic map and skein module framework.

Derived a 2+1-G-HQFT from the G-chromatic category.

Connected the framework to modified Turaev-Viro invariants.

Abstract

For G a group, we present a G-graded version of chromatic maps and skein modules and use them to define a 2+1-G-HQFT out of a G-chromatic category. The construction applies to the representations of unrestricted quantum groups at root of unity and recovers the modified Turaev-Viro 3-dimensional invariants.