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Swallowtail, Whitney Umbrella and Convex Hulls
Journal of Dynamical and Control Systems ( IF 0.9 ) Pub Date : 2020-08-25 , DOI: 10.1007/s10883-020-09510-5 Vyacheslav D. Sedykh
中文翻译:
燕尾,惠特尼伞和凸包
更新日期:2020-08-25
Journal of Dynamical and Control Systems ( IF 0.9 ) Pub Date : 2020-08-25 , DOI: 10.1007/s10883-020-09510-5 Vyacheslav D. Sedykh
One of the singularities of the convex hull of a generic hypersurface in \(\mathbb {R}^{4}\) leads to a generic sewing of two famous surfaces, the swallowtail and the Whitney umbrella, along their self-intersection lines. We prove that germs of all such sewings at the common endpoint of the self-intersection lines are diffeomorphic to each other with respect to diffeomorphisms of the ambient space.
中文翻译:
燕尾,惠特尼伞和凸包
\(\ mathbb {R} ^ {4} \)中通用超曲面的凸包的奇异点之一导致沿其自相交线对两个著名曲面(燕尾和惠特尼雨伞)进行通用缝合。我们证明,在自相交线的公共端点处,所有此类缝制的细菌相对于周围空间的微分形都是互异的。