Journal of Mathematical Physics, Analysis, Geometry
2021, vol. 17, No 2, pp. 119-145     ( to contents , go back )

A Kastler-Kalau-Walze Type Theorem for 7-Dimensional Manifolds with Boundary about Witten Deformation

Kai Hua Bao

School of Mathematics and Physics, Inner Mongolia University for the Nationalities, TongLiao, 028005, P. R. China

Ai Hui Sun

College of Mathematics, Jilin Normal University, Siping, 136000, P. R. China

Kun Ming Hu

School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China

Received February 3, 2020, revised March 13, 2020.


In the paper, we give a brute-force proof of the Kastler-Kalau-Walze type theorem for 7-dimensional manifolds with boundary about the Witten deformation and give a theoretical explanation of the gravitational action for 7 dimensional manifolds with boundary.

Mathematics Subject Classification 2010: 58G20, 53A30, 46L87
Key words: Witten deformation, noncommutative residue for manifolds with boundary, lower dimensional volumes

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