Triangulated Manifolds with Few Vertices: Combinatorial Manifolds
Frank H. Lutz
TL;DR
This survey explores the combinatorial properties of triangulated manifolds, focusing on lower bounds for vertices and cataloging known minimal triangulations.
Contribution
It compiles known lower bounds and examples of vertex-minimal triangulations, providing a comprehensive overview of the field.
Findings
Identified key lower bounds on vertex counts for triangulated manifolds.
Compiled a list of all known minimal triangulations.
Summarized the current state of combinatorial manifold research.
Abstract
In this survey on combinatorial properties of triangulated manifolds we discuss various lower bounds on the number of vertices of simplicial and combinatorial manifolds. Moreover, we give a list of all known examples of vertex-minimal triangulations.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Advanced Graph Theory Research