On the Loop Homology of a Certain Complex of RNA Structures

In this paper, we establish a topological framework of τ-structures to quantify the evolutionary transitions between two RNA sequence–structure pairs. developed here consist pair secondary structures together with non-crossing partial matching backbones. The loop complex τ-structure captures intersections loops in both structures. We compute homology τ-structures. show that only zeroth, first and second groups are free. particular, prove rank group equals number γ certain arc-components is given by γ−χ+1, where χ Euler characteristic complex.