Van Kampen-Flores theorem and Stiefel-Whitney classes

2023/04/17 by Kishimoto, Daisuke, Matsushita, Takahiro
#Algebraic Topology (math.AT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2304.08043

Abstract

The van Kampen-Flores theorem states that the d-skeleton of a (2d+2)-simplex does not embed into 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 ℝ^2d.

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