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A Poincaré–Hopf type formula for Chern character numbers

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Abstract

For two complex vector bundles admitting a homomorphism with isolated singularities between them, we establish a Poincaré–Hopf type formula for the difference of the Chern character numbers of these two vector bundles. As a consequence, we extend the original Poincaré–Hopf index formula to the case of complex vector fields.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Chongqing University of Technology, 400050, Chongqing, People’s Republic of China

    Huitao Feng

  2. Department of Mathematics, Oklahoma State University, Stillwater, OK, 74078-1058, USA

    Weiping Li

  3. Chern Institute of Mathematics and LPMC, Nankai University, 300071, Tianjin, People’s Republic of China

    Weiping Zhang

Authors
  1. Huitao Feng
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  2. Weiping Li
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  3. Weiping Zhang
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Corresponding author

Correspondence to Huitao Feng.

Additional information

H. Feng was partially supported by NNSFC, MOEC and NSFC and W. Zhang was partially supported by NNSFC and MOEC.

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Feng, H., Li, W. & Zhang, W. A Poincaré–Hopf type formula for Chern character numbers. Math. Z. 269, 401–410 (2011). https://doi.org/10.1007/s00209-010-0742-1

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  • DOI: https://doi.org/10.1007/s00209-010-0742-1

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