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Proper holomorphic maps from the unit disk to some unit ball

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 Added by John D'Angelo
 Publication date 2016
  fields
and research's language is English




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We study proper rational maps from the unit disk to balls in higher dimensions. After gathering some known results, we study the moduli space of unitary equivalence classes of polynomial proper maps from the disk to a ball, and we establish a normal form for these equivalence classes. We also prove that all rational proper maps from the disk to a ball are homotopic in target dimension at least $2$.



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