# 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 $2(k-3)-1$.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-01335381
Contributor : Carlos Simpson <>
Submitted on : Tuesday, June 21, 2016 - 9:33:43 PM
Last modification on : Tuesday, December 10, 2019 - 10:29:39 AM

### Identifiers

• HAL Id : hal-01335381, version 1
• ARXIV : 1504.05395

### Citation

Carlos Simpson. The dual boundary complex of the $SL_2$ character variety of a punctured sphere. 2015. ⟨hal-01335381⟩

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