What is the intersection of the vertices of a face of a simplicial complex?
$begingroup$
I am currently reading "Subgroup graph methods for presentations of finitely generated groups and the contractibility of associated simplicial complexes" By Cora Welsch and I'm a bit stuck with Theorem 5.6.
She considers a subcomplex $U$ of the nerve complex $NC(G,H_{fi})$.
I dont understand why:
- There always exists a finite set $Sigma$ consisting of all maximal simplices of $U$?
- What is the intersection of the vertices of an element $ sigma in Sigma $? (She denotes it by $cap sigma$.)
Thanks in advance!
group-theory group-presentation simplicial-complex
edited Dec 3 '18 at 1:15
Shaun
9,246113684
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
$endgroup$
add a comment |
$begingroup$
I am currently reading "Subgroup graph methods for presentations of finitely generated groups and the contractibility of associated simplicial complexes" By Cora Welsch and I'm a bit stuck with Theorem 5.6.
She considers a subcomplex $U$ of the nerve complex $NC(G,H_{fi})$.
I dont understand why:
- There always exists a finite set $Sigma$ consisting of all maximal simplices of $U$?
- What is the intersection of the vertices of an element $ sigma in Sigma $? (She denotes it by $cap sigma$.)
Thanks in advance!
group-theory group-presentation simplicial-complex
edited Dec 3 '18 at 1:15
Shaun
9,246113684
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
$endgroup$
add a comment |
$begingroup$
I am currently reading "Subgroup graph methods for presentations of finitely generated groups and the contractibility of associated simplicial complexes" By Cora Welsch and I'm a bit stuck with Theorem 5.6.
She considers a subcomplex $U$ of the nerve complex $NC(G,H_{fi})$.
I dont understand why:
- There always exists a finite set $Sigma$ consisting of all maximal simplices of $U$?
- What is the intersection of the vertices of an element $ sigma in Sigma $? (She denotes it by $cap sigma$.)
Thanks in advance!
group-theory group-presentation simplicial-complex
edited Dec 3 '18 at 1:15
Shaun
9,246113684
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
$endgroup$
I am currently reading "Subgroup graph methods for presentations of finitely generated groups and the contractibility of associated simplicial complexes" By Cora Welsch and I'm a bit stuck with Theorem 5.6.
She considers a subcomplex $U$ of the nerve complex $NC(G,H_{fi})$.
I dont understand why:
- There always exists a finite set $Sigma$ consisting of all maximal simplices of $U$?
- What is the intersection of the vertices of an element $ sigma in Sigma $? (She denotes it by $cap sigma$.)
Thanks in advance!
group-theory group-presentation simplicial-complex
group-theory group-presentation simplicial-complex
edited Dec 3 '18 at 1:15
Shaun
9,246113684
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
edited Dec 3 '18 at 1:15
Shaun
9,246113684
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
edited Dec 3 '18 at 1:15
Shaun
9,246113684
edited Dec 3 '18 at 1:15
Shaun
9,246113684
edited Dec 3 '18 at 1:15
Shaun
9,246113684
9,246113684
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
111
add a comment |
add a comment |
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