The coefficient body of Bell representations of finitely connected planar domains

Abstract

In this note, we determine the homotopy type of the coefficient body of Bell representations of non-degenerate n-connected planar domains with n ≥ 3. Also, by considering the isomorphism classes of rational functions, we get the precise number of those corresponding to Bell representations wth the same set of critical values. Further, the case of those with the same set of critical points is discussed.

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