Four dimensions from two in symplectic topology

2002/10/02 by Margaret Symington, Symington, Margaret · 7 citations
Mathematics · #53D05 #57M99 (Secondary) #57R15 (Primary) 55R55 #FOS: Mathematics #Geometric Topology (math.GT) #Symplectic Geometry (math.SG) #math.GT #math.SG #msc:53D05 #msc:55R55 #msc:57M99 #msc:57R15

paper · pdf · doi:10.48550/arxiv.math/0210033

51 pages, 18 figures

arxiv created 2002/10/02 · arxiv updated 2009/11/30

Abstract

This paper introduces two-dimensional diagrams that are slight generalizations of moment map images for toric four-manifolds and catalogs techniques for reading topological and symplectic properties of a symplectic four-manifold from these diagrams. The paper offers a purely topological approach to toric manifolds as well as methods for visualizing other manifolds, including the K3 surface, and for visualizing certain surgeries. Most of the techniques extend to higher dimensions.

Cited by

• Lectures on stabilized ellipsoid embeddings
• Semitoric Families on Pentagon Spaces
• Almost toric fibrations on symplectic blow ups
• ECH capacities of concave singular toric domains
• Semi-orthogonality in Fukaya-Seidel mirrors to blowups of abelian varieties
• Non-Affine Stein Manifolds and Normal Crossing Divisors
• Tetraplectic structures compatible with local quaternionic toric actions

Related

• Delzant-type classification of near-symplectic toric 4-manifolds
• Six Lectures on Four 4-Manifolds
• Recent developments in toric geometry
• Symplectic maps and hyperKähler moment map geometry
• Counting toric actions on symplectic four-manifolds