The loop homology algebra of discrete torsion

TL;DR

This paper investigates the algebraic structure of orbifold loop products and coproducts, linking them to group cohomology classes, and identifies conditions under which these products are trivial, advancing understanding in orbifold topology.

Contribution

It provides a new description of orbifold loop products and coproducts via group cohomology and computes conditions for their triviality, offering novel insights into orbifold loop algebra.

Findings

Orbifold loop product can be described by a group cohomology class.

In some cases, the orbifold loop product is trivial.

The paper links algebraic structures to topological invariants in orbifolds.

Abstract

We show that Lupercio-Uribe-Xicot\'{e}ncatl's orbifold loop product and coproduct can be described by a group cohomology class in some cases. By computing this cohomology class, we show that in some cases the orbifold loop product is trivial.