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
E-mail: baokh505@nenu.edu.cn

Ai Hui Sun

College of Mathematics, Jilin Normal University, Siping, 136000, P. R. China
E-mail: sunaihui2002@126.com

Kun Ming Hu

School of Mathematics and Statistics, Northeast Normal University, Changchun, 130024, P. R. China
E-mail: 2943220150@qq.com

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

Abstract

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