Weighted spectra on a weighted geometric realization of 2-simplexes and 3-simplexes.

In this paper, we construct a weighted geometric realization of the set of 2-simplexes and 3-simplexes. On this weighted geometric realization, we create the Laplacian associated to 2-simplexes L S 2 and the Laplacian associated to 3-simplexes L S 3 . We prove that the nonzero spectrum of L S 2 is the same as the nonzero spectrum of L S 3 . For 0, we show that 0 belongs to the spectrum of L S 2 or to the spectrum of L S 3 . [ABSTRACT FROM AUTHOR]