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 | References | Similar Articles | Additional Information

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 .

**[AR03]**Alejandro Adem and Yongbin Ruan,*Twisted orbifold 𝐾-theory*, Comm. Math. Phys.**237**(2003), no. 3, 533–556. MR**1993337**, 10.1007/s00220-003-0849-x**[ARZ]**A. Adem, Y. Ruan, and B. Zhang.

A stringy product on twisted orbifold -theory.

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An example of a twisted fusion algebra.

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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

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.