论文标题
有限确定的细菌的交叉盖，三重点和连接不变
Cross-caps, triple points and a linking invariant for finitely determined germs
论文作者
论文摘要
It was recently proved that for finitely determined germs $ Φ: ( \mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(Φ)$ of Whitney umbrella points and the number $T(Φ)$ of triple values of a stable deformation are topological invariants.该证明使用以下事实：组合$ c（φ）-3t（φ）$是拓扑的，因为它等于Ekholm和szűcs引入的相关浸入$ s^3 \ looparrowright s^5 $的链接不变。我们为这种平等提供了新的直接证明。我们还阐明了后一个不变的各种定义之间的关系。
It was recently proved that for finitely determined germs $ Φ: ( \mathbb{C}^2, 0) \to ( \mathbb{C}^3, 0) $ the number $C(Φ)$ of Whitney umbrella points and the number $T(Φ)$ of triple values of a stable deformation are topological invariants. The proof uses the fact that the combination $C(Φ)-3T(Φ)$ is topological since it equals the linking invariant of the associated immersion $S^3 \looparrowright S^5$ introduced by Ekholm and Szűcs. We provide a new, direct proof for this equality. We also clarify the relation between various definitions of the latter invariant.
