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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Acyclic embeddings of open Riemann surfaces into new examples of elliptic manifolds
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by Tyson Ritter PDF
Proc. Amer. Math. Soc. 141 (2013), 597-603 Request permission

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
  • Received by editor(s): July 4, 2011
  • Published electronically: June 21, 2012
  • Communicated by: Franc Forstneric
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2996964