Exhausting curve complexes by finite rigid sets on nonorientable surfaces (Q6561476)

From the abstract: ``Let \(N\) be a compact, connected, nonorientable surface of genus \(g\) with \(n\) boundary components. Let \(\mathcal{C}(N)\) be the curve complex of \(N\). We prove that if \((g,n)=(3,0)\) or \(g+n\geq5\), then there is an exhaustion of \(\mathcal{C}(N)\) by a sequence of finite rigid sets'' (improving the author's result on exhaustion of \(C(N)\) by a sequence of finite superrigid sets [\textit{E. Irmak}, Fundam. Math. 255, No. 2, 111--138 (2021; Zbl 1483.57014)]). \N\NHere a subcomplex \(\mathcal{B}\) is \textit{rigid} if every locally injective simplicial map \(\mathcal{B} \to C(N)\) is induced by a homeomorphism of \(N\). For orientable surfaces, the existence of finite rigid subcomplexes was proved by \textit{J. Aramayona} and \textit{C. J. Leininger} [J. Topol. Anal. 5, No. 2, 183--203 (2013; Zbl 1277.57017)], as well as the existence of an exhaustion of the curve complex by a sequence of finite rigid sets [\textit{J. Aramayona} and \textit{C. J. Leininger}, Pac. J. Math. 282, No. 2, 257--283 (2016; Zbl 1342.57015)].