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