scholarly journals Generalized complex Hamiltonian torus actions: examples and constraints

2010 ◽  
Vol 81 (3) ◽  
pp. 573-588
Author(s):  
Thomas Baird ◽  
Yi Lin
Keyword(s):  
Torus Actions ◽  
Hamiltonian Torus Actions ◽  
Generalized Complex

scholarly journals Convexity for Hamiltonian torus actions on $b$-symplectic manifolds

2017 ◽  
Vol 24 (2) ◽  
pp. 363-377 ◽  
Author(s):  
Victor Guillemin ◽  
Eva Miranda ◽  
Ana Rita Pires ◽  
Geoffrey Scott
Keyword(s):  
Symplectic Manifolds ◽  
Torus Actions ◽  
Hamiltonian Torus Actions

scholarly journals On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

2009 ◽  
Vol 89 (2) ◽  
pp. 101-113 ◽  
Author(s):  
Hans-Christian Herbig ◽  
Srikanth B. Iyengar ◽  
Markus J. Pflaum
Keyword(s):  
Star Products ◽  
Torus Actions ◽  
Quotient Spaces ◽  
Hamiltonian Torus Actions

scholarly journals Rigid subsets of symplectic manifolds

2009 ◽  
Vol 145 (03) ◽  
pp. 773-826 ◽  
Author(s):  
Michael Entov ◽  
Leonid Polterovich
Keyword(s):  
Symplectic Manifold ◽  
Lagrangian Submanifolds ◽  
Symplectic Manifolds ◽  
Smooth Functions ◽  
Torus Actions ◽  
Moment Maps ◽  
Quantum Homology ◽  
Singular Sets ◽  
Hamiltonian Torus Actions ◽  
Commutative Subalgebras

AbstractWe show that there is an hierarchy of intersection rigidity properties of sets in a closed symplectic manifold: some sets cannot be displaced by symplectomorphisms from more sets than the others. We also find new examples of rigidity of intersections involving, in particular, specific fibers of moment maps of Hamiltonian torus actions, monotone Lagrangian submanifolds (following the works of P. Albers and P. Biran-O. Cornea) as well as certain, possibly singular, sets defined in terms of Poisson-commutative subalgebras of smooth functions. In addition, we get some geometric obstructions to semi-simplicity of the quantum homology of symplectic manifolds. The proofs are based on the Floer-theoretical machinery of partial symplectic quasi-states.

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