Modified symmetrized integral in $G$-coalgebras

TL;DR

This paper introduces a new method for constructing invariants of G-colored 3-manifolds using Hopf G-coalgebra techniques and the concept of modified integral, advancing topological quantum field theory.

Contribution

It provides a novel Hopf G-coalgebra framework for G-colored 3-manifold invariants based on the modified integral concept.

Findings

Constructed G-colored 3-manifold invariants using Hopf G-coalgebras.

Established a purely algebraic approach with modified integrals.

Enhanced understanding of topological invariants in quantum topology.

Abstract

For $G$ a commutative group, we give a purely Hopf $G$-coalgebra construction of $G$-colored $3$-manifolds invariants using the notion of modified integral.