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Let $ (x_1,…,x_n)$ be the coordinate of $ \mathbb R^n$ . Define $ x_{-i}=(x_1,x_2,…,x_{i-1},x_{i+1},…,x_n)$ . The n-dimensional cross is defined to be a geometric object consist of $ n$ different $ (n-1)$ -manifolds that intersect at one unique point $ p$ . Each manifold $ \mathcal M_i$ (embedded in $ \mathbb R^n$ ) is shapedRead more