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On double vector bundles

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Abstract

In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.

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Authors and Affiliations

  1. Department of Mathematics, Tsinghua University, Beijing, 100084, P. R. China

    Zhuo Chen

  2. Department of Mathematics and LMAM, Peking University, Beijing, 100871, P. R. China

    Zhang Ju Liu

  3. Department of Mathematics, Jilin University, Changchun, 130012, P. R. China

    Yun He Sheng

Authors
  1. Zhuo Chen
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  2. Zhang Ju Liu
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  3. Yun He Sheng
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Corresponding author

Correspondence to Yun He Sheng.

Additional information

Supported by National Natural Science Foundation of China (Grant Nos. 11001146, 11101179) and the Beijing Higher Education Young Elite Teacher Project

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Chen, Z., Liu, Z.J. & Sheng, Y.H. On double vector bundles. Acta. Math. Sin.-English Ser. 30, 1655–1673 (2014). https://doi.org/10.1007/s10114-014-2412-4

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  • DOI: https://doi.org/10.1007/s10114-014-2412-4

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