In this paper, we analyze the homology of the simplicial complex induced by a given pair of RNA secondary structures, R = (S, T). Such a pair induces a bi-secondary structure, whose associated loop nerve X is the simplicial complex obtained by loop intersections. We will provide an algebraic proof of the fact that H-1(X) = 0. We will provide a combinatorial interpretation for the generators of H-2 (X) in terms of crossing components of the bi-structure and establish that the rank of H-2 (X) equals the total number of such crossing components. Finally, we shall prove that each crossing component naturally encodes a triangulation of a 2-sphere and provide an analysis of the geometric realization of X.
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