The dual boundary complex of the $SL_2$ character variety of a punctured sphere - Université Côte d'Azur Access content directly
Preprints, Working Papers, ... Year : 2016

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

Carlos Simpson

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 $2(k-3)-1$.

Dates and versions

hal-01331631 , version 1 (14-06-2016)

Identifiers

Cite

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

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More