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arXiv · 0706.3229

Stringy product on twisted orbifold K-theory for abelian quotients

Edward Becerra·Bernardo Uribe
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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 $(\integer/2)^3$.

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Edward Becerra, Bernardo Uribe. 2008-02-15. Stringy product on twisted orbifold K-theory for abelian quotients. https://arxiv.org/abs/0706.3229

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