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Jul 16, 2018 at 6:53 comment added RKS Thanks a lot for the reference of Xicotencatl. I believe that there is some kind of method to check whether such an algebraically defined map (when fiber is non-compact) is a locally trivial fibration? But no luck so far!
Jul 13, 2018 at 10:17 comment added Mark Grant The space in question is an orbit configuration space $F_{C_2}(\mathbb{C}^*,n)$, where the cyclic group $C_2$ acts by $x\mapsto x^{-1}$. Xicotencatl showed that orbit configuration spaces $F_G(M,n)$ have Fadell-Neuwirth fibrations, but only in the case when $G$ acts freely on $M$. This makes me think you should try to prove non-asphericity by looking for a sphere in $X_n$ enclosing a singular point, such as $(1,1)$.
Jul 11, 2018 at 11:17 history edited RKS
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Jul 9, 2018 at 6:32 history asked RKS CC BY-SA 4.0