Differential forms and the Wodzicki residue for manifolds with boundary

In [A. Connes, Quantized calculus and applications, XIth International Congress of Mathematical Physics (Paris,1994), 15–36, Internat Press, Cambridge, MA, 1995], Connes found a conformal invariant using Wodzicki’s 1-density and computed it in the case of 4-dimensional manifold without boundary. In [W. J. Ugalde, Differential forms and the Wodzicki residue, arXiv: Math, DG/0211361], Ugalde generalized the Connes’ result to n-dimensional manifold without boundary. In this paper, we generalize the results of [A. Connes, Quantized calculus and applications, XIth International Congress of Mathematical Physics (Paris,1994), 15–36, Internat Press, Cambridge, MA, 1995] and [W. J. Ugalde, Differential forms and the Wodzicki residue, arXiv: Math, DG/0211361] to the case of manifolds with boundary.