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 $2(k-3)-1$.
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https://hal.univ-cotedazur.fr/hal-01331631
Contributor : Jean-Louis Thomin <>
Submitted on : Tuesday, June 14, 2016 - 11:05:22 AM
Last modification on : Thursday, May 3, 2018 - 1:32:58 PM

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

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

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