Graph-encoded 3-manifolds

DOI10.1016/0012-365X(85)90179-7zbMath0585.57009OpenAlexW1966036101MaRDI QIDQ1070585

Arnaldo Mandel, Sóstenes Lins

Publication date: 1985

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0012-365x(85)90179-7

zbMATH Keywords

3-manifoldscrystallizationsball complex4-regular edge-colored graphsgraph-encoded manifoldsPoincaré's sphere

Mathematics Subject Classification ID

Related Items (34)

Lins-Mandel manifolds as branched coverings of \(S^ 3\) ⋮ Handles in graphs and sphere bundles over \(S^ 1\) ⋮ A graph-theoretical representation of PL-manifolds -- a survey on crystallizations ⋮ A homology theory for colored graphs ⋮ Manifold structures on abstract regular polytopes ⋮ Lins-Mandel graphs representing 3-manifolds ⋮ An effective algorithm to get linking numbers of 3-manifolds ⋮ Multiple residues in dimension three ⋮ Compact 3-manifolds via 4-colored graphs ⋮ On some properties of the groups G(n,l) ⋮ n-graphs ⋮ Counting gluings of octahedra ⋮ On the fundamental group of 3-gems and a `planar' class of 3-manifolds ⋮ Twistors: Bridges among 3-manifolds ⋮ Colorful polytopes and graphs ⋮ 4-Colored Triangulation of 3-Maps ⋮ Some bounds for the regular genus of PL-manifolds ⋮ Graphs encoding 3-manifolds of genus 2 ⋮ Decomposition of the vertex group of 3-manifolds ⋮ Branched coverings ⋮ Combinatorial handles and manifolds with boundary ⋮ Ghost symmetry and an analogue of Steinitz's theorem ⋮ Computing Turaev-Viro invariants for 3-manifolds ⋮ Invariant groups on equivalent crystallizations ⋮ 2-symmetric crystallizations and 2-fold branched coverings of \(S^ 3\) ⋮ On the groups of some fibered spaces ⋮ Open problems on graphs arising from geometric topology ⋮ On the cyclic coverings of the knot 5₂ ⋮ BLOBS AND FLIPS ON GEMS ⋮ Partial duality of hypermaps ⋮ Topological aspects of edge fusions in 4-graphs ⋮ Contracted \(k\)-tessellations of closed surfaces ⋮ Lins-Mandel crystallizations ⋮ A simple proof of Gagliardi's handle recognition theorem

Cites Work

• Recognizing a 3-dimensional handle among 4-coloured graphs
• Crystallisation moves
• On the genus of 4-dimensional products of manifolds
• A simple proof of Gagliardi's handle recognition theorem
• Paintings: a planar approach to higher dimensions
• On the fundamental group of 3-gems and a `planar' class of 3-manifolds
• A sequence representation for maps
• Graph-encoded maps
• Regular imbeddings of edge-coloured graphs
• Combinatorial maps
• An \(n\)-tet graph approach for non-guillotine packings of \(n\)-dimensional boxes into an \(n\)-container
• On the division of Euclidean n -space by topological ( n ─ 1)-spheres
• Extending the Concept of Genus to Dimension N
• THE PROBLEM OF DISCRIMINATING ALGORITHMICALLY THE STANDARD THREE-DIMENSIONAL SPHERE
• Closed 3-Manifolds With no Periodic Maps
• Crystallisations of 2-Fold Branched Coverings of S 3
• How to Draw a Graph
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