Stringy product on twisted orbifold K-theory for abelian quotients

TL;DR

This paper develops a model to compute the stringy product in twisted orbifold K-theory for abelian quotients, connecting it with Chen-Ruan cohomology and providing explicit calculations for weighted projective orbifolds and finite abelian group quotients.

Contribution

It introduces a new explicit model for calculating the stringy product on twisted orbifold K-theory for abelian orbifolds, including a decomposition formula for twisted cases.

Findings

Explicit description of the obstruction bundle.

Relation with Jarvis-Kaufmann-Kimura product and Chen-Ruan cohomology.

Calculations for weighted projective orbifolds and $( ext{Z}/2)^3$ group quotients.

Abstract

In this paper we present a model to calculate the stringy product on twisted orbifold K-theory of Adem-Ruan-Zhang for abelian complex orbifolds. In the first part we consider the non-twisted case on an orbifold presented as the quotient of a manifold acted by a compact abelian Lie group. We give an explicit description of the obstruction bundle, we explain the relation with the product defined by Jarvis-Kaufmann-Kimura and, via a Chern character map, with the Chen-Ruan cohomology, and we explicitely calculate the stringy product for a weighted projective orbifold. In the second part we consider orbifolds presented as the quotient of a manifold acted by a finite abelian group and twistings coming from the group cohomology. We show a decomposition formula for twisted orbifold K-theory that is suited to calculate the stringy product and we use this formula to calculate two examples when the group is $(\integer/2)^3$.