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

Abstract : 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 $2(k-3)-1$.
Type de document :
Pré-publication, Document de travail
2016
Domaine :

https://hal.univ-cotedazur.fr/hal-01331631
Contributeur : Jean-Louis Thomin <>
Soumis le : mardi 14 juin 2016 - 11:05:22
Dernière modification le : jeudi 11 janvier 2018 - 16:14:54

### Identifiants

• HAL Id : hal-01331631, version 1
• ARXIV : 1504.05395

### Citation

Carlos Simpson. The dual boundary complex of the $SL_2$ character variety of a punctured sphere. 2016. 〈hal-01331631〉

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