Mixing
What is the ring and does $phi^*$ preserves module operations
$begingroup$
I have posted this problem recently and I think that as it was too long, not many people took interest in it. So I am reposting it also I am giving you an earlier link :I had a problem in manifold which states:
Show that $A^1:Man^{op} to Mod$ is a functor, where $M$ is a manifold, $A^1(M)$ is the $1$-form on $M$. and for $phi:M to N$, $A^1(phi)=phi^*$. This means to show that
a) $A^1(M)$ is a module.(What is the ring?)
b) $phi^*$ preserves module operations(does the ring change?)(I feel yes! but not getting why!!)
c)$(1_M)^*=1_{A^1(M)}$
In part c) I feel that I have to show $w circ (Bbb 1_M)_*=(Bbb 1_{A^1(M)}w$ as $w circ (Bbb 1_M)_*=(Bbb 1_M)^*w$ but how!! Please help me in a), b) and c). Especially I feel that the ring in a) should be $Bbb R$
real-analysis differential-geometry manifolds smooth-manifolds manifolds-with-boundary
asked Jan 23 at 18:56
GimgimGimgim
29813
$endgroup$
add a comment |
$begingroup$
I have posted this problem recently and I think that as it was too long, not many people took interest in it. So I am reposting it also I am giving you an earlier link :I had a problem in manifold which states:
Show that $A^1:Man^{op} to Mod$ is a functor, where $M$ is a manifold, $A^1(M)$ is the $1$-form on $M$. and for $phi:M to N$, $A^1(phi)=phi^*$. This means to show that
a) $A^1(M)$ is a module.(What is the ring?)
b) $phi^*$ preserves module operations(does the ring change?)(I feel yes! but not getting why!!)
c)$(1_M)^*=1_{A^1(M)}$
In part c) I feel that I have to show $w circ (Bbb 1_M)_*=(Bbb 1_{A^1(M)}w$ as $w circ (Bbb 1_M)_*=(Bbb 1_M)^*w$ but how!! Please help me in a), b) and c). Especially I feel that the ring in a) should be $Bbb R$
real-analysis differential-geometry manifolds smooth-manifolds manifolds-with-boundary
asked Jan 23 at 18:56
GimgimGimgim
29813
$endgroup$
$begingroup$
1) $Bbb R$ 2) ?? 3) tautological if you know the definition of pullback
$endgroup$
– user98602
Jan 24 at 15:00
$begingroup$
Sorry, I am messed in the conception. Can you please explain in details? This will be of great help, as manifolds goes above my head.
$endgroup$
– Gimgim
Jan 26 at 5:01
$begingroup$
I suggest that you look at a smooth manifolds book, such as John Lee's "Introduction to Smooth Manifolds".
$endgroup$
– user98602
Jan 26 at 17:08
$begingroup$
Yes, I am reading that and Lee and Tu's book but this subject is hard at least to me. So it would of great help if you can expand me. Thanks anyway
$endgroup$
– Gimgim
Jan 27 at 2:18
add a comment |
$begingroup$
I have posted this problem recently and I think that as it was too long, not many people took interest in it. So I am reposting it also I am giving you an earlier link :I had a problem in manifold which states:
Show that $A^1:Man^{op} to Mod$ is a functor, where $M$ is a manifold, $A^1(M)$ is the $1$-form on $M$. and for $phi:M to N$, $A^1(phi)=phi^*$. This means to show that
a) $A^1(M)$ is a module.(What is the ring?)
b) $phi^*$ preserves module operations(does the ring change?)(I feel yes! but not getting why!!)
c)$(1_M)^*=1_{A^1(M)}$
In part c) I feel that I have to show $w circ (Bbb 1_M)_*=(Bbb 1_{A^1(M)}w$ as $w circ (Bbb 1_M)_*=(Bbb 1_M)^*w$ but how!! Please help me in a), b) and c). Especially I feel that the ring in a) should be $Bbb R$
real-analysis differential-geometry manifolds smooth-manifolds manifolds-with-boundary
asked Jan 23 at 18:56
GimgimGimgim
29813
$endgroup$
I have posted this problem recently and I think that as it was too long, not many people took interest in it. So I am reposting it also I am giving you an earlier link :I had a problem in manifold which states:
Show that $A^1:Man^{op} to Mod$ is a functor, where $M$ is a manifold, $A^1(M)$ is the $1$-form on $M$. and for $phi:M to N$, $A^1(phi)=phi^*$. This means to show that
a) $A^1(M)$ is a module.(What is the ring?)
b) $phi^*$ preserves module operations(does the ring change?)(I feel yes! but not getting why!!)
c)$(1_M)^*=1_{A^1(M)}$
In part c) I feel that I have to show $w circ (Bbb 1_M)_*=(Bbb 1_{A^1(M)}w$ as $w circ (Bbb 1_M)_*=(Bbb 1_M)^*w$ but how!! Please help me in a), b) and c). Especially I feel that the ring in a) should be $Bbb R$
real-analysis differential-geometry manifolds smooth-manifolds manifolds-with-boundary
real-analysis differential-geometry manifolds smooth-manifolds manifolds-with-boundary
asked Jan 23 at 18:56
GimgimGimgim
29813
asked Jan 23 at 18:56
GimgimGimgim
29813
edited Jan 26 at 5:00
Gimgim
asked Jan 23 at 18:56
GimgimGimgim
29813
asked Jan 23 at 18:56
GimgimGimgim
29813
asked Jan 23 at 18:56
GimgimGimgim
29813
29813
$begingroup$
1) $Bbb R$ 2) ?? 3) tautological if you know the definition of pullback
$endgroup$
– user98602
Jan 24 at 15:00
$begingroup$
Sorry, I am messed in the conception. Can you please explain in details? This will be of great help, as manifolds goes above my head.
$endgroup$
– Gimgim
Jan 26 at 5:01
$begingroup$
I suggest that you look at a smooth manifolds book, such as John Lee's "Introduction to Smooth Manifolds".
$endgroup$
– user98602
Jan 26 at 17:08
$begingroup$
Yes, I am reading that and Lee and Tu's book but this subject is hard at least to me. So it would of great help if you can expand me. Thanks anyway
$endgroup$
– Gimgim
Jan 27 at 2:18
add a comment |
$begingroup$
1) $Bbb R$ 2) ?? 3) tautological if you know the definition of pullback
$endgroup$
– user98602
Jan 24 at 15:00
$begingroup$
Sorry, I am messed in the conception. Can you please explain in details? This will be of great help, as manifolds goes above my head.
$endgroup$
– Gimgim
Jan 26 at 5:01
$begingroup$
I suggest that you look at a smooth manifolds book, such as John Lee's "Introduction to Smooth Manifolds".
$endgroup$
– user98602
Jan 26 at 17:08
$begingroup$
Yes, I am reading that and Lee and Tu's book but this subject is hard at least to me. So it would of great help if you can expand me. Thanks anyway
$endgroup$
– Gimgim
Jan 27 at 2:18
$begingroup$
1) $Bbb R$ 2) ?? 3) tautological if you know the definition of pullback
$endgroup$
– user98602
Jan 24 at 15:00
$begingroup$
1) $Bbb R$ 2) ?? 3) tautological if you know the definition of pullback
$endgroup$
– user98602
Jan 24 at 15:00
$begingroup$
Sorry, I am messed in the conception. Can you please explain in details? This will be of great help, as manifolds goes above my head.
$endgroup$
– Gimgim
Jan 26 at 5:01
$begingroup$
Sorry, I am messed in the conception. Can you please explain in details? This will be of great help, as manifolds goes above my head.
$endgroup$
– Gimgim
Jan 26 at 5:01
$begingroup$
I suggest that you look at a smooth manifolds book, such as John Lee's "Introduction to Smooth Manifolds".
$endgroup$
– user98602
Jan 26 at 17:08
$begingroup$
I suggest that you look at a smooth manifolds book, such as John Lee's "Introduction to Smooth Manifolds".
$endgroup$
– user98602
Jan 26 at 17:08
$begingroup$
Yes, I am reading that and Lee and Tu's book but this subject is hard at least to me. So it would of great help if you can expand me. Thanks anyway
$endgroup$
– Gimgim
Jan 27 at 2:18
$begingroup$
Yes, I am reading that and Lee and Tu's book but this subject is hard at least to me. So it would of great help if you can expand me. Thanks anyway
$endgroup$
– Gimgim
Jan 27 at 2:18
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%2f3084907%2fwhat-is-the-ring-and-does-phi-preserves-module-operations%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%2f3084907%2fwhat-is-the-ring-and-does-phi-preserves-module-operations%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
$begingroup$
1) $Bbb R$ 2) ?? 3) tautological if you know the definition of pullback
$endgroup$
– user98602
Jan 24 at 15:00
$begingroup$
Sorry, I am messed in the conception. Can you please explain in details? This will be of great help, as manifolds goes above my head.
$endgroup$
– Gimgim
Jan 26 at 5:01
$begingroup$
I suggest that you look at a smooth manifolds book, such as John Lee's "Introduction to Smooth Manifolds".
$endgroup$
– user98602
Jan 26 at 17:08
$begingroup$
Yes, I am reading that and Lee and Tu's book but this subject is hard at least to me. So it would of great help if you can expand me. Thanks anyway
$endgroup$
– Gimgim
Jan 27 at 2:18