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The Quarterly Journal of Mathematics Advance Access published online on August 4, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap024
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

NON-KÄHLER SYMPLECTIC MANIFOLDS WITH TORIC SYMMETRIES

Yi Lin {dagger}

Department of Mathematical Sciences, Georgia Southern University, 203 Georgia Ave., Statesboro, GA 30460, USA

Alvaro Pelayo{ddagger}

Mathematics Department, University of California–Berkeley, 970 Evans Hall # 3840, Berkeley, CA 94720-3840, USA

{ddagger} Corresponding author. E-mail: apelayo{at}math.berkeley.edu

Received 23 February 2009; revised 19 June 2009
  Abstract

Drawing on the classification of symplectic manifolds with coisotropic principal orbits by Duistermaat and Pelayo, in this note we exhibit families of compact symplectic manifolds, such that: (i) no two manifolds in a family are homotopically equivalent; (ii) each manifold in each family possesses Hamiltonian, and non-Hamiltonian, toric symmetries; (iii) each manifold has odd first Betti number and hence it is not a Kähler manifold. This can be viewed as an application of the aforementioned classification.

{dagger} E-mail: yilin{at}georgiasouthern.edu


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