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arXiv · 1504.05395

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

Carlos Simpson
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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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Carlos Simpson. 2015-04-21. The dual boundary complex of the $SL_2$ character variety of a punctured sphere. https://arxiv.org/abs/1504.05395

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