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
8,883113681
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
8,883113681
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
8,883113681
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
8,883113681
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
edited Dec 3 '18 at 1:15
Shaun
8,883113681
asked Jan 13 '18 at 14:09
Lau_GrvLau_Grv
111
edited Dec 3 '18 at 1:15
Shaun
8,883113681
edited Dec 3 '18 at 1:15
Shaun
8,883113681
edited Dec 3 '18 at 1:15
Shaun
8,883113681
8,883113681
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 |
0
active
oldest
votes
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2603592%2fwhat-is-the-intersection-of-the-vertices-of-a-face-of-a-simplicial-complex%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
0
active
oldest
votes
0
active
oldest
votes
active
oldest
votes
active
oldest
votes
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2603592%2fwhat-is-the-intersection-of-the-vertices-of-a-face-of-a-simplicial-complex%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
