Holomorphic motions commuting with semigroups

Volume 119 / 1996

Zbigniew Słodkowski Studia Mathematica 119 (1996), 1-16 DOI: 10.4064/sm-119-1-1-16


A holomorphic family $f_z$, |z|<1, of injections of a compact set E into the Riemann sphere can be extended to a holomorphic family of homeomorphisms $F_z$, |z|<1, of the Riemann sphere. (An earlier result of the author.) It is shown below that there exist extensions $F_z$ which, in addition, commute with some holomorphic families of holomorphic endomorphisms of $ℂ̅̅̅̅̅̅ \ f_z(E)$, |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.


  • Zbigniew Słodkowski

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