Download or read book Symplectic Actions of $2$-Tori on $4$-Manifolds written by Alvaro Pelayo and published by American Mathematical Soc.. This book was released on 2010-02-22 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.