We herein investigate the homotopy types of the independence complexes of square grid graphs with cylindrical identification for and . We show that they are all homotopy equivalent to a wedge of spheres.
"On the homotopy types of the independence complexes of grid graphs with cylindrical identification." Kyoto J. Math. 52 (3) 479 - 501, Fall 2012. https://doi.org/10.1215/21562261-1625172