Abstract
In this paper, we establish a general Kastler–Kalau–Walze type theorem for any dimensional manifolds with boundary which generalizes the results in [Y. Wang, Lower-dimensional volumes and Kastler–Kalau–Walze type theorem for manifolds with boundary, Commun. Theor. Phys. 54 (2010) 38–42]. This solves a problem of the referee of [J. Wang and Y. Wang, A Kastler–Kalau–Walze type theorem for five-dimensional manifolds with boundary, Int. J. Geom. Meth. Mod. Phys. 12(5) (2015), Article ID: 1550064, 34 pp.], which is a general expression of the lower dimensional volumes in terms of the geometric data on the manifold.
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