论文标题
通过符号能力识别对象
Recognition of objects through symplectic capacities
论文作者
论文摘要
我们证明，广义的符号能力识别符号类别中的对象，其对象的形式为$（m，ω）$，因此$ m $是紧凑型和1个连接的歧管，$ω$是$ m $的确切符号形式，并且存在$ m $ $ m $的边界。因此，一组广义的符号能力是此类类别的完全不变。这回答了Cieliebak，Hofer，Latschev和Schlenk的问题。除了$ \ mathbb {r}^4 $中的歧管，椭圆形和polydiscs的识别结果外，这似乎是有关此问题的第一个结果。令人惊讶的是，我们的结果对于差异形式类别更普遍。因此，对象的识别不是符合性现象。 我们还证明了标准化能力的结果版本。
We prove that the generalized symplectic capacities recognize objects in symplectic categories whose objects are of the form $(M, ω)$, such that $M$ is a compact and 1-connected manifold, $ω$ is an exact symplectic form on $M$, and there exists a boundary component of $M$ with negative helicity. The set of generalized symplectic capacities is thus a complete invariant for such categories. This answers a question by Cieliebak, Hofer, Latschev, and Schlenk. It appears to be the first result concerning this question, except for recognition results for manifolds of dimension 2, ellipsoids, and polydiscs in $\mathbb{R}^4$. Strikingly, our result holds more generally for differential form categories. Recognition of objects is therefore not a symplectic phenomenon. We also prove a version of the result for normalized capacities.
