Pseudoholomorphic curves and the symplectic isotopy problem
Pseudoholomorphic curves and the symplectic isotopy problem
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发表时间：
2000-10
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通讯作者：
V. Shevchishin
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作者：
V. Shevchishin
研究了拟全纯曲线的变形问题以及拟全纯曲线的全模空间的有关几何性质。给出了全模空间鞍点性质的一个充分条件。对于嵌入伪全纯曲线的情形，建立并求解了局部辛同伦问题。证明了Cp^2中任意两个同阶辛嵌入曲面Sigma_0、Sigma_1都是辛同位素的。
The deformation problem for pseudoholomorphic curves and related geometrical properties of the total moduli space of pseudoholomorphic curves are studied. A sufficient condition for the saddle point property of the total moduli space is established. The local symplectic isotopy problem is formulated and solved for the case of imbedded pseudoholomorphic curves. It is shown that any two symplectically imbedded surfaces Sigma_0, Sigma_1 in CP^2 of the same degree d\le 6 are symplectically isotopic.