Graphs and Their Clique Complexes Are Pseudotopological Weakly Homotopy Equivalent
arXiv:2406.00149
Abstract
We establish a connection between the graphs and their geometric realizations of their clique complexes, proving that graphs with their canonical pseudotopological structure, are weakly homotopy equivalent to the geometric realization of their clique complex.
24 pages, 4 figures. We change the notation a bit, prioritizing the focus on pseudotopological spaces. We add brief discussion section