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The Noncommutative Residue about Witten Deformation

  • Kai Hua BaoEmail author
  • Ai Hui Sun
  • Chao Deng
Article
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Abstract

In this paper, we compute lower dimensional volumes Vol 4 (1,1) and Vol 6 (2,2) about Witten deformation for 4, 6-dimensional spin manifolds with boundary respectively, and get assosiated Kastler–Kalau–Walze type theorems. We also give theoritic explaination of the gravitational action for 4, 6 dimensional manifolds with boundary by these noncommutative residues.

Keywords

Lower-dimensional volumes noncommutative residue gravitational action Witten deformation 

MR(2010) Subject Classification

58G20 53A30 46L87 

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Notes

Acknowledgements

This work is supported by Science Foundation for BS423 and Inner Mongolia Natural Science Foundation: No. 2018LHO1004. The author also thank the referee for his (or her) careful reading and helpful comments.

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science (CAS), Chinese Mathematical Society (CAS) and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsIneer Mongolia University for NationnalitiesTongliaoP. R. China
  2. 2.College of MathematicsJilin Normal UniversitySipingP. R. China
  3. 3.School of Mathematics and StatisticsNortheast Normal UniversityChangchunP. R. China

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