Double points and the proper transform in symplectic geometry

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• 作者：McCarthy ; John D. ; Wolfson ; Jon G.
• 关键词：Symplectic singularities ; blowing up ; proper transform ; 32S45 ; 58F05
• 刊名：Differential Geometry and its Applications
• 出版年：1996
• 出版时间：July, 1996
• 年：1996
• 卷：6
• 期：2
• 页码：101-107
• 全文大小：365 K

文摘

In his book, Partial Differential Relations, Gromov introduced the symplectic analogue of the complex analytic operations of blowing up and blowing down. Gromov proposed, in Sect. 3.4.4(D) of Partial Differential Relations, a program for resolving the singularities of symplectic immersions with symplectic crossings via blowing up, in exact analogue with the well known complex analytic technique. The purpose of this note is to show that this program cannot work. We show that there are symplectically immersed surfaces in symplectic 4-manifolds which do not have a symplettically embedded proper transform in any blow up of the four manifold.