The dual boundary complex of the $SL_2$ character variety of a punctured sphere

Carlos T. Simpson (1)

1 LJAD - Laboratoire Jean Alexandre Dieudonné

Suppose $C_1,\ldots , C_k$ are generic conjugacy classes in $SL_2({\mathbb C})$. Consider the character variety of local systems on ${\mathbb P}^1-\{ y_1,\ldots , y_k\}$ whose monodromy transformations around the punctures $y_i$ are in the respective conjugacy classes $C_i$. We show that the dual boundary complex of this character variety is homotopy equivalent to a sphere of dimension $2(k-3)-1$.

Domaines: Géométrie algébrique [math.AG]

Carlos T. Simpson. The dual boundary complex of the $SL_2$ character variety of a punctured sphere. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2016, In honour of Vadim Schechtman’s 60th birthday, 25 (2-3), pp.317-361. ⟨10.5802/afst.1496⟩. ⟨hal-01335381⟩