Are the manifolds $N=(mathbb{R},text{Id})$ and $M=(mathbb{R},xmapsto x^{frac{1}{3}})$ diffeomorphic?
$begingroup$
Are the manifolds $N=(mathbb{R},text{Id})$ and $M=(mathbb{R},xmapsto x^{frac{1}{3}})$ diffeomorphic?
I have already shown that $text{Id}: N rightarrow M$ is a homeomorphism but not a diffeomorphism.
differential-geometry smooth-manifolds diffeomorphism
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
$endgroup$
add a comment |
$begingroup$
Are the manifolds $N=(mathbb{R},text{Id})$ and $M=(mathbb{R},xmapsto x^{frac{1}{3}})$ diffeomorphic?
I have already shown that $text{Id}: N rightarrow M$ is a homeomorphism but not a diffeomorphism.
differential-geometry smooth-manifolds diffeomorphism
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
$endgroup$
add a comment |
$begingroup$
Are the manifolds $N=(mathbb{R},text{Id})$ and $M=(mathbb{R},xmapsto x^{frac{1}{3}})$ diffeomorphic?
I have already shown that $text{Id}: N rightarrow M$ is a homeomorphism but not a diffeomorphism.
differential-geometry smooth-manifolds diffeomorphism
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
$endgroup$
Are the manifolds $N=(mathbb{R},text{Id})$ and $M=(mathbb{R},xmapsto x^{frac{1}{3}})$ diffeomorphic?
I have already shown that $text{Id}: N rightarrow M$ is a homeomorphism but not a diffeomorphism.
differential-geometry smooth-manifolds diffeomorphism
differential-geometry smooth-manifolds diffeomorphism
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
asked Dec 20 '18 at 12:14
Jens WagemakerJens Wagemaker
550312
550312
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Yes. Try to show that $F:Nto M$ given by $F(x)=x^3$ is a diffeomorphism.
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
$endgroup$
add a comment |
$begingroup$
Yes, they are diffeomorphic. Consider the map$$begin{array}{ccc}N&longrightarrow&M\x&mapsto&x^3.end{array}$$It's a diffeomorphism.
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
$endgroup$
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%2f3047474%2fare-the-manifolds-n-mathbbr-textid-and-m-mathbbr-x-mapsto-x-fra%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes. Try to show that $F:Nto M$ given by $F(x)=x^3$ is a diffeomorphism.
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
$endgroup$
add a comment |
$begingroup$
Yes. Try to show that $F:Nto M$ given by $F(x)=x^3$ is a diffeomorphism.
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
$endgroup$
add a comment |
$begingroup$
Yes. Try to show that $F:Nto M$ given by $F(x)=x^3$ is a diffeomorphism.
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
$endgroup$
Yes. Try to show that $F:Nto M$ given by $F(x)=x^3$ is a diffeomorphism.
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
answered Dec 20 '18 at 12:18
positrón0802positrón0802
4,353520
4,353520
add a comment |
add a comment |
$begingroup$
Yes, they are diffeomorphic. Consider the map$$begin{array}{ccc}N&longrightarrow&M\x&mapsto&x^3.end{array}$$It's a diffeomorphism.
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
$endgroup$
add a comment |
$begingroup$
Yes, they are diffeomorphic. Consider the map$$begin{array}{ccc}N&longrightarrow&M\x&mapsto&x^3.end{array}$$It's a diffeomorphism.
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
$endgroup$
add a comment |
$begingroup$
Yes, they are diffeomorphic. Consider the map$$begin{array}{ccc}N&longrightarrow&M\x&mapsto&x^3.end{array}$$It's a diffeomorphism.
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
$endgroup$
Yes, they are diffeomorphic. Consider the map$$begin{array}{ccc}N&longrightarrow&M\x&mapsto&x^3.end{array}$$It's a diffeomorphism.
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
answered Dec 20 '18 at 12:17
José Carlos SantosJosé Carlos Santos
162k22128232
162k22128232
add a comment |
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%2f3047474%2fare-the-manifolds-n-mathbbr-textid-and-m-mathbbr-x-mapsto-x-fra%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
