Spectral gap of a weighted 3-simplicial complex.

In this paper, we construct a new framework that's we call the weighted 3 -simplicial complex and we define its spectral gap. An upper bound for our spectral gap is given by generalizing the Cheeger constant. The lower bound for our spectral gap is obtained from the first nonzero eigenvalue of the Laplacian acting on the functions of certain weighted 2 -simplicial complexes. [ABSTRACT FROM AUTHOR]