Stable homotopy, $1$-dimensional NCCW complexes, and Property (H) - An, Qingnan; Elliott, George A.; Liu, Zhichao; Zhang, Yuanhang (MATHEMATICA SCANDINAVICA, 2020)
In this paper, we show that the homomorphisms between two unital one-dimensional NCCW complexes with the same KK-class are stably homotopic, that is, after adding on a common homomorphism (with finite dimensional image), they are homotopic. As a consequence, any one-dimensional NCCW complex has the Property (H).