Stringy product on twisted orbifold K-theory for abelian quotients

Becerra, Edward; Uribe, Bernardo

doi:10.1090/S0002-9947-09-04760-6

Stringy product on twisted orbifold K-theory for abelian quotients
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by Edward Becerra and Bernardo Uribe PDF

Trans. Amer. Math. Soc. 361 (2009), 5781-5803 Request permission

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, we explicitly 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 $(\mathbb {Z}/2)^3$.

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