Polyhedral realization in R3 of triangulations of the torus and 2-manifolds in cyclic 4-polytopes

Amos Altshuler

doi:10.1016/0012-365X(71)90011-2

Polyhedral realization in R³ of triangulations of the torus and 2-manifolds in cyclic 4-polytopes

Amos Altshuler

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

Given a map M on a 2-manifold of genus ≥1, it is generally not known when is the map geometrically embeddable in R³. Sufficient conditions are given here in case M is a triangulation of the torus. Those conditions are based on Hamiltonian circuits of certain types and on other circuits in the given map. In the general case, sufficient conditions of a different nature are given. Also, the 2-dimensional skeletons of the cyclic 4-polytopes are studied, from the point of view of the 2-manifolds contained in them.

Original language	English
Pages (from-to)	211-238
Number of pages	28
Journal	Discrete Mathematics
Volume	1
Issue number	3
DOIs	https://doi.org/10.1016/0012-365X(71)90011-2
State	Published - 1 Jan 1971
Externally published	Yes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/0012-365X(71)90011-2

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abstract = "Given a map M on a 2-manifold of genus ≥1, it is generally not known when is the map geometrically embeddable in R3. Sufficient conditions are given here in case M is a triangulation of the torus. Those conditions are based on Hamiltonian circuits of certain types and on other circuits in the given map. In the general case, sufficient conditions of a different nature are given. Also, the 2-dimensional skeletons of the cyclic 4-polytopes are studied, from the point of view of the 2-manifolds contained in them.",

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AB - Given a map M on a 2-manifold of genus ≥1, it is generally not known when is the map geometrically embeddable in R3. Sufficient conditions are given here in case M is a triangulation of the torus. Those conditions are based on Hamiltonian circuits of certain types and on other circuits in the given map. In the general case, sufficient conditions of a different nature are given. Also, the 2-dimensional skeletons of the cyclic 4-polytopes are studied, from the point of view of the 2-manifolds contained in them.

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Polyhedral realization in R³ of triangulations of the torus and 2-manifolds in cyclic 4-polytopes

Abstract

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