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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Stringy product on twisted orbifold K-theory for abelian quotients


Authors: Edward Becerra and Bernardo Uribe
Journal: Trans. Amer. Math. Soc. 361 (2009), 5781-5803
MSC (2000): Primary 14N35, 19L47; Secondary 55N15, 55N91
Published electronically: June 4, 2009
MathSciNet review: 2529914
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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, 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 $ (\ensuremath{{\mathbb{Z}}}/2)^3$.


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Additional Information

Edward Becerra
Affiliation: Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia
Email: es.becerra75@uniandes.edu.co

Bernardo Uribe
Affiliation: Departamento de Matemáticas, Universidad de los Andes, Carrera 1 N. 18A - 10, Bogotá, Colombia
Email: buribe@uniandes.edu.co

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04760-6
PII: S 0002-9947(09)04760-6
Keywords: Stringy product, twisted orbifold K-theory, Chen-Ruan cohomology, inverse transgression map
Received by editor(s): June 27, 2007
Published electronically: June 4, 2009
Additional Notes: Both authors acknowledge the support of COLCIENCIAS through the grant 120440520246 and of CONACYT-COLCIENCIAS throught contract number 376-2007
The second author was partially supported by the “Fondo de apoyo a investigadores jovenes” from Universidad de los Andes
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.