Finite rigid sets and homologically non-trivial spheres in the curve complex of a surface

Joan Birman, Nathan Broaddus, William Menasco

Aramayona and Leininger have provided a "finite rigid subset" $\mathfrak{X}(\Sigma )$ of the curve complex $\mathcal{C}(\Sigma )$ of a surface $\Sigma ={\Sigma }_g^n$, characterized by the fact that any si…