TY - JOUR
T1 - Non-Käler Symplectic Manifolds with Toric Symmetries
AU - Lin, Yi
AU - Pelayo, Alvaro
PY - 2011/3/1
Y1 - 2011/3/1
N2 - 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.
AB - 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.
KW - Non-Käler symplectic manifolds
KW - Toric symmetries
UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/99
UR - https://doi.org/10.1093/qmath/hap024
U2 - 10.1093/qmath/hap024
DO - 10.1093/qmath/hap024
M3 - Article
VL - 62
JO - The Quarterly Journal of Mathematics
JF - The Quarterly Journal of Mathematics
ER -