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nonmanifold Why are these vertices and edges considered nonmanifold? What is the correct name for these surfaces(other than nonmanifold)?

Glorfindel
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pusheax
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1 Answers1

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They are not manifolds because they do not fulfiull the definition. Specifically, they do not "look like $\mathbb R^n$" in the marked parts. They qualify as CW complexes, however.

Hagen von Eitzen
  • 374,180
  • Thanks for the anwser! I have further questions if you don't mind. Is neighbourhood of non-manifold vertice not open? And neighbourhood of non-manifold edge is not homeomorphic to disk? Can these surfaces be called algebraic varieties(which have singular points as opposed to manifolds)? – pusheax Apr 21 '14 at 13:13
  • They are also simplicial complexes. @pusheax: They are not algebraic varieties: Such a variety has the property that link of every point has even Euler characteristic. In particular, this link cannot be contractible. – Moishe Kohan Apr 23 '14 at 00:05