Quasi-Lie bialgebras of loops in quasi-surfaces

TL;DR

This paper introduces a new algebraic structure called a quasi-Lie bialgebra on loops in quasi-surfaces, expanding the understanding of loop operations in topological spaces.

Contribution

It establishes that natural operations on loops in quasi-surfaces form a quasi-Lie bialgebra, a novel algebraic framework for these topological objects.

Findings

Loops in quasi-surfaces can be equipped with a quasi-Lie bialgebra structure.

The algebraic operations on loops are compatible with the quasi-Lie bialgebra axioms.

This framework generalizes classical Lie algebra structures to a broader topological context.

Abstract

We discuss natural operations on loops in a quasi-surface and show that these operations define a structure of a quasi-Lie bialgebra in the module generated by the set of free homotopy classes of non-contractible loops.