Symplectic Actions of 2-Tori on 4-Manifolds (Memoirs of the American Mathematical Society)
Author： Alvaro Pelayo
Publisher： American Mathematical Society
Publication year： 2013
E-ISBN: 9781470405731
P-ISBN(Paperback): 9780821847138
P-ISBN(Hardback): 9780821847138
Subject： O189.3 analytical topology
Keyword： Geometry and Topology
Language： ENG
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Symplectic Actions of 2-Tori on 4-Manifolds (Memoirs of the American Mathematical Society)
Description
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.