Holomorphic motions commuting with semigroups

Słodkowski, Zbigniew

Studia Mathematica, Tome 119 (1996), p. 1-16 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $ℂ ̅ ̅ ̅ ̅ ̅ ̅ f_{z} (E)$ , |z|<1 (under suitable assumptions). The classes of covering maps and maps with the path lifting property are discussed.

Publié le : 1996-01-01

Zbl 0865.30023

EUDML-ID : urn:eudml:doc:216283

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     title = {Holomorphic motions commuting with semigroups},
     journal = {Studia Mathematica},
     volume = {119},
     year = {1996},
     pages = {1-16},
     zbl = {0865.30023},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv119i1p1bwm}
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Słodkowski, Zbigniew. Holomorphic motions commuting with semigroups. Studia Mathematica, Tome 119 (1996) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv119i1p1bwm/

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