Are triangulations of compact manifolds PL homeomorphic?
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I have frequently come across the statement "Any two triangulations of a compact n-manifold are related by bistellar moves" attributed to Pachner via Lickorish's paper 'Simplicial moves on complexes and manifolds'. The theorem this refer to is the following: Closed combinatorial n-manifolds are PL homeomorphic if and only if they are bistellar equivalent.
My question is: Considering that Hauptvermutung is not true for manifolds of dimension more than 3, how can we justify this statement?
gt.geometric-topology simplicial-complexes triangulations combinatorial-topology
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I have frequently come across the statement "Any two triangulations of a compact n-manifold are related by bistellar moves" attributed to Pachner via Lickorish's paper 'Simplicial moves on complexes and manifolds'. The theorem this refer to is the following: Closed combinatorial n-manifolds are PL homeomorphic if and only if they are bistellar equivalent.
My question is: Considering that Hauptvermutung is not true for manifolds of dimension more than 3, how can we justify this statement?
gt.geometric-topology simplicial-complexes triangulations combinatorial-topology
asked 1 hour ago
user136604user136604
262
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
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add a comment |
$begingroup$
I have frequently come across the statement "Any two triangulations of a compact n-manifold are related by bistellar moves" attributed to Pachner via Lickorish's paper 'Simplicial moves on complexes and manifolds'. The theorem this refer to is the following: Closed combinatorial n-manifolds are PL homeomorphic if and only if they are bistellar equivalent.
My question is: Considering that Hauptvermutung is not true for manifolds of dimension more than 3, how can we justify this statement?
gt.geometric-topology simplicial-complexes triangulations combinatorial-topology
asked 1 hour ago
user136604user136604
262
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
$endgroup$
I have frequently come across the statement "Any two triangulations of a compact n-manifold are related by bistellar moves" attributed to Pachner via Lickorish's paper 'Simplicial moves on complexes and manifolds'. The theorem this refer to is the following: Closed combinatorial n-manifolds are PL homeomorphic if and only if they are bistellar equivalent.
My question is: Considering that Hauptvermutung is not true for manifolds of dimension more than 3, how can we justify this statement?
gt.geometric-topology simplicial-complexes triangulations combinatorial-topology
gt.geometric-topology simplicial-complexes triangulations combinatorial-topology
asked 1 hour ago
user136604user136604
262
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
user136604user136604
262
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
user136604user136604
262
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 1 hour ago
user136604user136604
262
asked 1 hour ago
user136604user136604
262
262
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user136604 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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Pachner‘s Theorem is about PL-homeomorphic manifolds, while the Hauptvermutung is asking for a PL-homeomorphism between manifolds which a priori are only homeomorphic.
answered 1 hour ago
ThiKuThiKu
6,44512137
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1 Answer
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1 Answer
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$begingroup$
Pachner‘s Theorem is about PL-homeomorphic manifolds, while the Hauptvermutung is asking for a PL-homeomorphism between manifolds which a priori are only homeomorphic.
answered 1 hour ago
ThiKuThiKu
6,44512137
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add a comment |
$begingroup$
Pachner‘s Theorem is about PL-homeomorphic manifolds, while the Hauptvermutung is asking for a PL-homeomorphism between manifolds which a priori are only homeomorphic.
answered 1 hour ago
ThiKuThiKu
6,44512137
$endgroup$
add a comment |
$begingroup$
Pachner‘s Theorem is about PL-homeomorphic manifolds, while the Hauptvermutung is asking for a PL-homeomorphism between manifolds which a priori are only homeomorphic.
answered 1 hour ago
ThiKuThiKu
6,44512137
$endgroup$
Pachner‘s Theorem is about PL-homeomorphic manifolds, while the Hauptvermutung is asking for a PL-homeomorphism between manifolds which a priori are only homeomorphic.
answered 1 hour ago
ThiKuThiKu
6,44512137
answered 1 hour ago
ThiKuThiKu
6,44512137
answered 1 hour ago
ThiKuThiKu
6,44512137
answered 1 hour ago
ThiKuThiKu
6,44512137
6,44512137
add a comment |
add a comment |
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