Invariance of the Barycentric Subdivision of a Simplicial Complex
Rashid Zaare-Nahandi
TL;DR
This paper demonstrates that a simplicial complex can be uniquely identified by its barycentric subdivision or comparability graph, and reviews various invariants of simplicial complexes.
Contribution
It establishes the invariance of the simplicial complex's structure under barycentric subdivision and compares algebraic, combinatorial, and topological invariants.
Findings
Simplicial complex is uniquely determined by its barycentric subdivision.
Barycentric subdivision preserves the isomorphism class of the complex.
Several invariants of simplicial complexes are summarized.
Abstract
In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of simplicial complexes.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Topological and Geometric Data Analysis · Advanced Combinatorial Mathematics