The coefficient body of Bell representations of finitely connected planar domains

doi:10.1016/j.jmaa.2004.03.043

Journal of Mathematical Analysis and Applications

Volume 295, Issue 2, 15 July 2004, Pages 620-632

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Abstract

In this paper, 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 with same set of critical values. Further, the case of those with the same set of critical points is discussed.

Keywords

Conformal representation

Rational function

Hurwitz space

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¹: This work was supported by Grant R04-2003-000-10045-0 from the Korea Science and Engineering Foundation.