The coefficient body of Bell representations of finitely connected planar domains (Q596761)

Let \(\Omega\) be an \(n\)-connected subdomain of the Riemann sphere \(\hat{\mathbb C}\). It is known that \(\Omega\) can be mapped biholomorphically onto a domain of the form \[ \left \{z: \left | z+\sum_{k=1}^{n-1}\frac{a_k}{z-b_k}\right | <1 \right \} \] with suitable \(a_k,b_k\in \mathbb C,\; k=1,2,\dots, n-1\); see \textit{S. R. Bell} [Duke Math. J 98, No. 1, 187--207 (1999; Zbl 0948.30015)] and also \textit{M. Jeong} and \textit{M. Taniguchi} [Proc. Am. Math. Soc. 131, No. 8, 2325--2328 (2003; Zbl 1019.30005)]. Let \(B_n\subset \mathbb C^{2n-2}\) be the set of all possible \((2n-2)\)-tuples obtained in this way. This is \textit{the coefficient body for \(n\)-connected domains}. The authors investigate the geometric structure of \(B_n\). In particular they determine its homotopy type.