Abstract
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 [Formula: see text] and the Laplacian associated to 3-simplexes [Formula: see text]. We prove that the nonzero spectrum of [Formula: see text] is the same as the nonzero spectrum of [Formula: see text]. For 0, we show that 0 belongs to the spectrum of [Formula: see text] or to the spectrum of [Formula: see text].
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