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Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds


Author: Tyson Ritter
Journal: Proc. Amer. Math. Soc. 141 (2013), 597-603
MSC (2010): Primary 32Q40; Secondary 32E10, 32H02, 32H35, 32M17, 32Q28
DOI: https://doi.org/10.1090/S0002-9939-2012-11430-3
Published electronically: June 21, 2012
MathSciNet review: 2996964
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Abstract: 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 $ \mathbb{C}^n$ 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 Lárusson.


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Additional Information

Tyson Ritter
Affiliation: School of Mathematical Sciences, University of Adelaide, Adelaide SA 5005, Australia
Email: tyson.ritter@adelaide.edu.au

DOI: https://doi.org/10.1090/S0002-9939-2012-11430-3
Received by editor(s): July 4, 2011
Published electronically: June 21, 2012
Communicated by: Franc Forstneric
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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