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Barycentric subdivision

In mathematics, the barycentric subdivision is a standard way to subdivide a given simplex into smaller ones. Its extension to simplicial complexes is a canonical method to refining them. Therefore, the barycentric subdivision is an important tool in algebraic topology.

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Motivation

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Map overview Semantic statistics

Barycentric subdivision

Nodes31
Edges30
Triples51
Avg. degree1.94
Density0.064516
Components1

How this topic connects Entity context

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Barycentric subdivision

Top relations

related to Homology · 10
Barycentric subdivision → Delta, For, Here, In, Indeed, Moreover, On, Subdivision, This, To
related to Motivation · 9
Barycentric subdivision → Euler, Excision, In, Mayer, Moreover, One, The, This, Vietoris
related to Mesh · 8
Barycentric subdivision → Big, Bigl, Bigr, Delta, Let, One, Then, Therefore
related to Simplicial approximation · 7
Barycentric subdivision → By, Consider, Each, If, Lefschetz's, Let, The
related to Barycentric subdivision of a convex polytope · 5
Barycentric subdivision → For, In, The, This, Two
has application · 4
Barycentric subdivision → Mayer, The, Therefore, Vietoris
related to Barycentric subdivision of a simplex · 4
Barycentric subdivision → Delta, For, The, To
is a · 3
Barycentric subdivision → important tool in algebraic topology, operation on simplicial complexes, standard way to subdivide a given simplex into smaller ones

Important terminology Word statistics

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Important terminology

displaystyle subdivision simplicial barycentric simplex homology simplices one complexes delta groups complex rightarrow maps theorem continuous mathcal dimension map approximation

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Barycentric subdivisionis astandard way to subdivide a given simplex into smaller ones0.90text
Barycentric subdivisionis aimportant tool in algebraic topology0.90text
Barycentric subdivisionis aoperation on simplicial complexes0.90text
the Euler characteristic to the spacesinstance ofThis substitution allows one to assign combinatorial invariants0.80text
Barycentric subdivisionhas applicationThe0.60section
Barycentric subdivisionhas applicationTherefore0.60section
Barycentric subdivisionhas applicationMayer0.60section
Barycentric subdivisionhas applicationVietoris0.60section
Barycentric subdivisionrelated to Barycentric subdivision of a convex polytopeThe0.60section
Barycentric subdivisionrelated to Barycentric subdivision of a convex polytopeIn0.60section
Barycentric subdivisionrelated to Barycentric subdivision of a convex polytopeThis0.60section
Barycentric subdivisionrelated to Barycentric subdivision of a convex polytopeTwo0.60section

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