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arXiv · 1604.02395

Proving Tucker's Lemma with a Volume Argument

Beauttie Kuture·Oscar Leong·Christopher Loa·Mutiara Sondjaja·Francis Edward Su
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Abstract

Sperner's lemma is a statement about labeled triangulations of a simplex. McLennan and Tourky (2007) provided a novel proof of Sperner's Lemma by examining volumes of simplices in a triangulation under time-linear simplex-linear deformation. We adapt a similar argument to prove Tucker's Lemma on a triangulated cross-polytope $P$. The McLennan-Tourky technique does not directly apply because this deformation may distort the volume of $P$. We remedy this by inscribing $P$ in its dual polytope, triangulating it, and considering how the volumes of deformed simplices behave.

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Beauttie Kuture, Oscar Leong, Christopher Loa, Mutiara Sondjaja, Francis Edward Su. 2016-04-08. Proving Tucker's Lemma with a Volume Argument. https://arxiv.org/abs/1604.02395

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