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Symplectic actions of 2-tori on 4-manifolds

✍ Scribed by Alvaro Pelayo

Publisher
Amer Mathematical Society
Year
2010
Tongue
English
Leaves
96
Series
Memoirs of the American Mathematical Society 0959
Category
Library
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✦ Synopsis

In this paper the author classifies symplectic actions of $2$-tori on compact connected symplectic $4$-manifolds, up to equivariant symplectomorphisms. This extends results of Atiyah, Guillemin-Sternberg, Delzant and Benoist. The classification is in terms of a collection of invariants of the topology of the manifold, of the torus action and of the symplectic form. The author constructs explicit models of such symplectic manifolds with torus actions, defined in terms of these invariants

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