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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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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
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 5781-5803
  • MSC (2000): Primary 14N35, 19L47; Secondary 55N15, 55N91
  • DOI: https://doi.org/10.1090/S0002-9947-09-04760-6
  • MathSciNet review: 2529914