Hatcher-Thurston complex for surfaces with non-planar ends

In this paper, for each $k\in \mathbb{N}$, we define a complex ${\mathrm{\Gamma }}_k(S)$ for an infinite-type surface $S$ with non-planar ends, which serves as an analog of the Hatcher-Thurston complex for the infinite-type setting. We show that ${\mathrm{\Gamma }}_k(S)$ is connected, simply connected, and that the automorphism group of ${\mathrm{\Gamma }}_k(S)$ is isomorphic to the extended mapping class group.