A strong Oka principle for embeddings of some planar domains into CxC*

Details A strong Oka principle for embeddings of some planar domains into CxC* A strong Oka principle for embeddings of some planar domains into CxC*

2010-11-18

arxiv.org/abs/1011.4116v1

Mathematics

Complex Variables

25 pages

Scientific paper

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 CxC*, namely that every continuous map is homotopic to a proper holomorphic embedding. An important ingredient is a generalisation to CxC* of recent results of Wold and Forstneric on the long-standing problem of properly embedding open Riemann surfaces into C^2, with an additional result on the homotopy class of the embeddings. We also give a complete solution to a question that arises naturally in Larusson's holomorphic homotopy theory, of the existence of acyclic embeddings of Riemann surfaces with abelian fundamental group into 2-dimensional elliptic Stein manifolds.

Affiliated with

Also associated with

No associations

Rating

A strong Oka principle for embeddings of some planar domains into CxC* does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A strong Oka principle for embeddings of some planar domains into CxC*, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A strong Oka principle for embeddings of some planar domains into CxC* will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-536039