naa a22 4500 510811116 CHVBK 20180411083443.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1007/s12220-011-9254-4 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9254-4 Ritter Tyson School of Mathematical Sciences, University of Adelaide, 5005, Adelaide, SA, Australia aut A Strong Oka Principle for Embeddings of Some Planar Domains into ℂ×ℂ∗ [Elektronische Daten] [Tyson Ritter] Gromov, in his seminal 1989 paper on the Oka principle, introduced the notion of an elliptic manifold and proved that every continuous map from a Stein manifold to an elliptic manifold is homotopic to a holomorphic map. We show that a much stronger Oka principle holds in the special case of maps from certain open Riemann surfaces called circular domains into ℂ×ℂ∗, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalization to ℂ×ℂ∗ of recent results of Wold and Forstnerič on the long-standing problem of properly embedding open Riemann surfaces into ℂ2, with an additional result on the homotopy class of the embeddings. We also give a complete solution to a question that arises naturally in Lárusson's holomorphic homotopy theory, of the existence of acyclic embeddings of Riemann surfaces with abelian fundamental group into 2-dimensional elliptic Stein manifolds. Mathematica Josephina, Inc., 2011 Holomorphic embedding nationallicence Riemann surface nationallicence Oka principle nationallicence Stein manifold nationallicence Elliptic manifold nationallicence Acyclic map nationallicence Circular domain nationallicence Fatou-Bieberbach domain nationallicence Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 571-597 1050-6926 23:2<571 2013 23 12220 https://doi.org/10.1007/s12220-011-9254-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9254-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Ritter Tyson School of Mathematical Sciences, University of Adelaide, 5005, Adelaide, SA, Australia aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/2(2013-04-01), 571-597 1050-6926 23:2<571 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer