Is there a relationship between loop(topology) and loop(abstract algebra)
$begingroup$
It seems interesting that the term "loop" is used in both topology and abstract algebra. Is that just a coincidence, or is there a connection between them?
Everything I have seen in my research associates the topological idea of loop more to groups than abstract algebra loops.
abstract-algebra general-topology loop-spaces
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
$endgroup$
add a comment |
$begingroup$
It seems interesting that the term "loop" is used in both topology and abstract algebra. Is that just a coincidence, or is there a connection between them?
Everything I have seen in my research associates the topological idea of loop more to groups than abstract algebra loops.
abstract-algebra general-topology loop-spaces
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
$endgroup$
add a comment |
$begingroup$
It seems interesting that the term "loop" is used in both topology and abstract algebra. Is that just a coincidence, or is there a connection between them?
Everything I have seen in my research associates the topological idea of loop more to groups than abstract algebra loops.
abstract-algebra general-topology loop-spaces
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
$endgroup$
It seems interesting that the term "loop" is used in both topology and abstract algebra. Is that just a coincidence, or is there a connection between them?
Everything I have seen in my research associates the topological idea of loop more to groups than abstract algebra loops.
abstract-algebra general-topology loop-spaces
abstract-algebra general-topology loop-spaces
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
asked Dec 5 '18 at 15:54
Cort AmmonCort Ammon
2,381616
2,381616
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
The choice of word is probably just a coincidence. I haven't heard of any deep connection, nor can I spot one.
That is not to say that you can put a (algebra)loop structure on a set of (topology)loops. As you say, there are a few natural choices of operations between (topology)loops but those most often result in full-fledged groups.
Naming collisions like this happen all the time, of course. Consider "domain" and "regular" etc.
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
$endgroup$
1
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
add a comment |
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%2f3027232%2fis-there-a-relationship-between-looptopology-and-loopabstract-algebra%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
The choice of word is probably just a coincidence. I haven't heard of any deep connection, nor can I spot one.
That is not to say that you can put a (algebra)loop structure on a set of (topology)loops. As you say, there are a few natural choices of operations between (topology)loops but those most often result in full-fledged groups.
Naming collisions like this happen all the time, of course. Consider "domain" and "regular" etc.
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
$endgroup$
1
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
add a comment |
$begingroup$
The choice of word is probably just a coincidence. I haven't heard of any deep connection, nor can I spot one.
That is not to say that you can put a (algebra)loop structure on a set of (topology)loops. As you say, there are a few natural choices of operations between (topology)loops but those most often result in full-fledged groups.
Naming collisions like this happen all the time, of course. Consider "domain" and "regular" etc.
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
$endgroup$
1
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
add a comment |
$begingroup$
The choice of word is probably just a coincidence. I haven't heard of any deep connection, nor can I spot one.
That is not to say that you can put a (algebra)loop structure on a set of (topology)loops. As you say, there are a few natural choices of operations between (topology)loops but those most often result in full-fledged groups.
Naming collisions like this happen all the time, of course. Consider "domain" and "regular" etc.
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
$endgroup$
The choice of word is probably just a coincidence. I haven't heard of any deep connection, nor can I spot one.
That is not to say that you can put a (algebra)loop structure on a set of (topology)loops. As you say, there are a few natural choices of operations between (topology)loops but those most often result in full-fledged groups.
Naming collisions like this happen all the time, of course. Consider "domain" and "regular" etc.
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
answered Dec 5 '18 at 16:05
rschwiebrschwieb
106k12102249
106k12102249
1
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
add a comment |
1
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
1
1
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
$begingroup$
Also "kernel", "field", "normal"...
$endgroup$
– Giuseppe Negro
Dec 5 '18 at 16:07
add a comment |
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%2f3027232%2fis-there-a-relationship-between-looptopology-and-loopabstract-algebra%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
