NDLI: Non-existence of polyhedral immersions of triangulated surfaces in $$\mathbb R^3$$

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Non-existence of polyhedral immersions of triangulated surfaces in $$\mathbb R^3$$

Content Provider	Springer Nature Link
Author	Leopold, Undine
Copyright Year	2016
Abstract	We present and apply a method for disproving the existence of polyhedral immersions in $$\mathbb R^3$$ 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 $$\mathbb R^3$$ .
Starting Page	247
Ending Page	265
Page Count	19
File Format	PDF
ISSN	01384821
Journal	Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
Volume Number	58
Issue Number	2
e-ISSN	21910383
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2016-10-07
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Non-orientable surface Triangulation Geometric realization Polyhedral immersion Self-intersection Obstruction Neighborly Polyhedral manifolds Two-dimensional complexes Algebra Geometry Algebraic Geometry Convex and Discrete Geometry
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory Geometry and Topology

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