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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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Delocalized Chern character for stringy orbifold K-theory
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by Jianxun Hu and Bai-Ling Wang PDF
Trans. Amer. Math. Soc. 365 (2013), 6309-6341 Request permission

Abstract:

In this paper, we define a stringy product on $K^*_{orb}(\mathfrak {X}) \otimes \mathbb {C}$, the orbifold K-theory of any almost complex presentable orbifold $\mathfrak {X}$. We establish that under this stringy product, the delocalized Chern character \[ ch_{deloc} : K^*_{orb}(\mathfrak {X}) \otimes \mathbb {C} \longrightarrow H^*_{CR}(\mathfrak {X}), \] after a canonical modification, is a ring isomorphism. Here $H^*_{CR}(\mathfrak {X})$ is the Chen-Ruan cohomology of $\mathfrak {X}$. The proof relies on an intrinsic description of the obstruction bundles in the construction of the Chen-Ruan product. As an application, we investigate this stringy product on the equivariant K-theory $K^*_G(G)$ of a finite group $G$ with the conjugation action. It turns out that the stringy product is different from the Pontryagin product (the latter is also called the fusion product in string theory).
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Additional Information
  • Jianxun Hu
  • Affiliation: Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, People’s Republic of China
  • Email: stsjxhu@mail.sysu.edu.cn
  • Bai-Ling Wang
  • Affiliation: Department of Mathematics, Australian National University, Canberra ACT 0200, Australia
  • Email: bai-ling.wang@anu.edu.au
  • Received by editor(s): October 5, 2011
  • Received by editor(s) in revised form: March 19, 2012
  • Published electronically: June 4, 2013
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6309-6341
  • MSC (2010): Primary 57R19, 19L10, 22A22; Secondary 55N15, 53D45
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05834-5
  • MathSciNet review: 3105753