An Explicit View of the Hitchin Fibration on the Betti Side for ℙ1 minus Five Points

The dual complex of the divisor at infinity of the character variety of local systems on P1−{t1,…,t5} with monodromies in prescribed conjugacy classes Ci⊂SL2(C), was shown by Komyo to be the sphere S3. This chapter compares in some detail the projection from a tubular neighbourhood to this dual complex, with the corresponding Hitchin fibration at infinity.