Non-existence of polyhedral immersions of triangulated surfaces in ℝ³

2016/06/15 by Leopold, Undine
#52B70 #57M20 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1606.04848

Abstract

We present and apply a method for disproving the existence of polyhedral immersions in ℝ³ of certain triangulations on non-orientable surfaces. In particular, it is proved that neither of the two vertex-minimal, neighborly 9-vertex triangulations of the non-orientable surface of genus 5 are realizable as immersed polyhedral surfaces in ℝ³.

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