Delzant-type classification of near-symplectic toric 4-manifolds
Author(s)Kaufman, Samuel, 1981-
Massachusetts Institute of Technology. Dept. of Mathematics.
Victor W. Guillemin.
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Delzant's theorem for symplectic toric manifolds says that there is a one-to-one correspondence between certain convex polytopes in ... and symplectic toric 2n-manifolds, realized by the image of the moment map. I present proofs of this theorem and the convexity theorem of Atiyah-Guillemin-Sternberg on which it relies. Then, I describe Honda's results on the local structure of near-symplectic 4-manifolds, and inspired by recent work of Gay-Symington, I describe a generalization of Delzant's theorem to near-symplectic toric 4-manifolds. One interesting feature of the generalization is the failure of convexity, which I discuss in detail.
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2005.Includes bibliographical references (p. 65-66).
DepartmentMassachusetts Institute of Technology. Dept. of Mathematics.
Massachusetts Institute of Technology