2011/07/01 by Tyson Ritter, Ritter, Tyson
Mathematics · #32E10 #32H02 #32H35 #32M17 #32Q28 (Secondary) #32Q40 (Primary) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.CV #msc:32E10 #msc:32H02 #msc:32H35 #msc:32M17 #msc:32Q28 #msc:32Q40
paper · pdf · doi:10.48550/arxiv.1107.0102
7 pages
arxiv created 2011/07/01 · openalex publication_date 2011/07/01 · arxiv updated 2011/07/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The geometric notion of ellipticity for complex manifolds was introduced by Gromov in his seminal 1989 paper on the Oka principle, and is a sufficient condition for a manifold to be Oka. In the current paper we present contributions to three open questions involving elliptic and Oka manifolds. We show that quotients of Cn by discrete groups of affine transformations are elliptic. Combined with an example of Margulis, this yields new examples of elliptic manifolds with free fundamental groups and vanishing higher homotopy. Finally we show that every open Riemann surface embeds acyclically into an elliptic manifold, giving a partial answer to a question of Larusson.