Van Kampen-Flores定理与Stiefel-Whitney类
Van Kampen-Flores theorem and Stiefel-Whitney classes
AI总结：
该研究将经典van Kampen-Flores定理推广到满足Stiefel-Whitney类特定条件的流形三角剖分情形，证明总Stiefel-Whitney类非平凡的(2d+1)维流形三角剖分的d维骨架无法嵌入ℝ^{2d}。
摘要：
van Kampen-Flores定理指出，(2d+2)维单形的d维骨架无法嵌入到ℝ^{2d}中。我们针对满足Stiefel-Whitney类特定条件的流形三角剖分，证明了van Kampen-Flores定理。具体而言，我们证明了总Stiefel-Whitney类非平凡的(2d+1)维流形的三角剖分的d维骨架无法嵌入到ℝ^{2d}中。
英文摘要：
The van Kampen-Flores theorem states that the $d$-skeleton of a $(2d+2)$-simplex does not embed into $\mathbb{R}^{2d}$. We prove the van Kampen-Flores theorem for triangulations of manifolds satisfying a certain condition on their Stiefel-Whitney classes. In particular, we show that the $d$-skeleton of a triangulation of a $(2d+1)$-manifold with non-trivial total Stiefel-Whitney class does not embed into $\mathbb{R}^{2d}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
