论文标题
符合参数射线符合参数射线
Removing parametrized rays symplectically
论文作者
论文摘要
从同骨歧管中提取孤立的射线会导致对初始射线的歧管符号词。在附加条件下，具有更高尺寸的参数射线的相同。更确切地说，令$（m，ω）$为符号歧管。令$ [0，\ infty）\ times q \ subset \ mathbb {r} \ times q $被视为参数化射线$ [0，\ infty）$，让$φ：[ - 1，\ infty）\ times q \ to m $ to m $是注射性，适当的，适当的，持续的，持续的，连续的，连续的，连续的$（$）$（-1，\ sutty）。如果适用于标准向量字段$ \ frac {\ partial} {\ partial t} $ on $ \ mathbb {r} $以及任何其他的向量field $ν$ cangent $（ - 1，\ 1，\ infty）\ times q $方程$ m \ setMinusφ（[0，\ infty）\ times q）$是符号切除型。
Extracting isolated rays from a symplectic manifold result in a manifold symplectomorphic to the initial one. The same holds for higher dimensional parametrized rays under an additional condition. More precisely, let $(M,ω)$ be a symplectic manifold. Let $[0,\infty)\times Q\subset\mathbb{R}\times Q$ be considered as parametrized rays $[0,\infty)$ and let $φ:[-1,\infty)\times Q\to M$ be an injective, proper, continuous map immersive on $(-1,\infty)\times Q$. If for the standard vector field $\frac{\partial}{\partial t}$ on $\mathbb{R}$ and any further vector field $ν$ tangent to $(-1,\infty)\times Q$ the equation $φ^*ω(\frac{\partial}{\partial t},ν)=0$ holds then $M$ and $M\setminus φ([0,\infty)\times Q)$ are symplectomorphic.
