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Virtual manifolds and localization

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Abstract

In this paper, we explore the virtual technique that is very useful in studying the moduli problem from a differential geometric point of view. We introduce a class of new objects “virtual manifolds/orbifolds”, on which we develop the integration theory. In particular, the virtual localization formula is obtained.

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Authors and Affiliations

  1. Department of Mathematics and Yangtze Mathematical Center, Sichuan University, Chengdu, 610064, P. R. China

    Bohui Chen

  2. Department of Mathematics, Peking University, Beijing, 100084, P. R. China

    Gang Tian

  3. Department of Mathematics, Princeton University, Princeton, New Jersey, 08544-1000, USA

    Gang Tian

Authors
  1. Bohui Chen
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  2. Gang Tian
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Correspondence to Bohui Chen.

Additional information

The first author is supported by an NSF key project and a 973 project 2006CB805900

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Chen, B., Tian, G. Virtual manifolds and localization. Acta. Math. Sin.-English Ser. 26, 1–24 (2010). https://doi.org/10.1007/s10114-010-9538-9

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  • DOI: https://doi.org/10.1007/s10114-010-9538-9

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