Mixing
Computing Homology
I need A little bit more clarification when computing the homology of a chain complex. So the problem is:
Compute the simplicial homology of the graph with vertices $$V=left{ 1, 2, 3, 4 right}$$ and edges $$E=left { (1, 2)right }$$
Now, I know
$
H_{k}=frac{kerpartial _{k}}{impartial _{k+1}}
$
and I ‘m supposed to construct a matrix of the boundary maps, and that’s what confuses me.
I have that
$C_{0}=left {1, 2, 3, 4right }$ and $C_{1}=left {(1, 2)right }$.
And the boundary I got is $partial _{1}=C_{1}rightarrow C_{0}=2-1$, is this right? Also this is all done in $F_{2}$
topological-data-analysis
asked Nov 20 '18 at 2:10
LexyFidds
226
add a comment |
I need A little bit more clarification when computing the homology of a chain complex. So the problem is:
Compute the simplicial homology of the graph with vertices $$V=left{ 1, 2, 3, 4 right}$$ and edges $$E=left { (1, 2)right }$$
Now, I know
$
H_{k}=frac{kerpartial _{k}}{impartial _{k+1}}
$
and I ‘m supposed to construct a matrix of the boundary maps, and that’s what confuses me.
I have that
$C_{0}=left {1, 2, 3, 4right }$ and $C_{1}=left {(1, 2)right }$.
And the boundary I got is $partial _{1}=C_{1}rightarrow C_{0}=2-1$, is this right? Also this is all done in $F_{2}$
topological-data-analysis
asked Nov 20 '18 at 2:10
LexyFidds
226
1
So, that would be represented by a $1times 4$ matrix $$pmatrix{-1&1&0&0}.$$
– Lord Shark the Unknown
Nov 20 '18 at 4:49
add a comment |
I need A little bit more clarification when computing the homology of a chain complex. So the problem is:
Compute the simplicial homology of the graph with vertices $$V=left{ 1, 2, 3, 4 right}$$ and edges $$E=left { (1, 2)right }$$
Now, I know
$
H_{k}=frac{kerpartial _{k}}{impartial _{k+1}}
$
and I ‘m supposed to construct a matrix of the boundary maps, and that’s what confuses me.
I have that
$C_{0}=left {1, 2, 3, 4right }$ and $C_{1}=left {(1, 2)right }$.
And the boundary I got is $partial _{1}=C_{1}rightarrow C_{0}=2-1$, is this right? Also this is all done in $F_{2}$
topological-data-analysis
asked Nov 20 '18 at 2:10
LexyFidds
226
I need A little bit more clarification when computing the homology of a chain complex. So the problem is:
Compute the simplicial homology of the graph with vertices $$V=left{ 1, 2, 3, 4 right}$$ and edges $$E=left { (1, 2)right }$$
Now, I know
$
H_{k}=frac{kerpartial _{k}}{impartial _{k+1}}
$
and I ‘m supposed to construct a matrix of the boundary maps, and that’s what confuses me.
I have that
$C_{0}=left {1, 2, 3, 4right }$ and $C_{1}=left {(1, 2)right }$.
And the boundary I got is $partial _{1}=C_{1}rightarrow C_{0}=2-1$, is this right? Also this is all done in $F_{2}$
topological-data-analysis
topological-data-analysis
asked Nov 20 '18 at 2:10
LexyFidds
226
asked Nov 20 '18 at 2:10
LexyFidds
226
asked Nov 20 '18 at 2:10
LexyFidds
226
asked Nov 20 '18 at 2:10
LexyFidds
226
asked Nov 20 '18 at 2:10
LexyFidds
226
226
1
So, that would be represented by a $1times 4$ matrix $$pmatrix{-1&1&0&0}.$$
– Lord Shark the Unknown
Nov 20 '18 at 4:49
add a comment |
1
So, that would be represented by a $1times 4$ matrix $$pmatrix{-1&1&0&0}.$$
– Lord Shark the Unknown
Nov 20 '18 at 4:49
1
1
So, that would be represented by a $1times 4$ matrix $$pmatrix{-1&1&0&0}.$$
– Lord Shark the Unknown
Nov 20 '18 at 4:49
So, that would be represented by a $1times 4$ matrix $$pmatrix{-1&1&0&0}.$$
– Lord Shark the Unknown
Nov 20 '18 at 4:49
add a comment |
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%2f3005838%2fcomputing-homology%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
active
oldest
votes
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.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- 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.
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%2f3005838%2fcomputing-homology%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
1
So, that would be represented by a $1times 4$ matrix $$pmatrix{-1&1&0&0}.$$
– Lord Shark the Unknown
Nov 20 '18 at 4:49