Twisted K-Theory for the Orbifold [*/G]

TL;DR

This paper investigates the relationship between twisted orbifold K-theories for different orbifolds and demonstrates conditions under which these theories are isomorphic, advancing understanding in orbifold topology and twisted K-theory.

Contribution

It establishes an isomorphism between twisted orbifold K-theories for different orbifolds under specific hypotheses, extending the theoretical framework of twisted K-theory.

Findings

Proves isomorphism between twisted orbifold K-theories under certain conditions.

Identifies hypotheses on twists and groups for the isomorphism to hold.

Enhances understanding of relationships between orbifold K-theories.

Abstract

We study the relationship between the twisted Orbifold K-theories ${^{\alpha}}K_{orb}(\textsl{X})$ and ${^{\alpha'}}K_{orb}(\textsl{Y})$ for two different twists $\alpha\in Z^3(G;S^1)$ and $\alpha'\in Z^3(G';S^1)$ of the Orbifolds $\textsl{X}=[*/G]$ and $\textsl{Y}=[*/G']$ respectively, for $G$ and $G'$ finite groups. We prove that under suitable hypothesis over the twisting $\alpha'$ and the group $G'$ we obtain an isomorphism between these twisted K-theories.