Higher cup-1 product of coboundaries is also a coboundary? The 2019 Stack Overflow Developer Survey Results Are InPontrjagin square (Mosher and Tangora Question)The complement of a Cartesian product for characterizing the closed sets of a product spaceGroup cohomology: cup product for cyclic groupsCohomology ring of a direct sum via Poincare dualityDoes the cup product on de Rham cohomology induce a nondegenerate bilinear form?Reference Request: Equivariant cup product in singular cohomologyNotational issues with group cohomologyLinking number and cup productDoes $H^bullet(G, mathbbZ)$ have a coalgebra structure?singular cohomology and Poincaré duality
What does Linus Torvalds mean when he says that Git "never ever" tracks a file?
What did it mean to "align" a radio?
Loose spokes after only a few rides
Is there any way to tell whether the shot is going to hit you or not?
What do the Banks children have against barley water?
Can we generate random numbers using irrational numbers like π and e?
Have you ever entered Singapore using a different passport or name?
How to notate time signature switching consistently every measure
Is this app Icon Browser Safe/Legit?
For what reasons would an animal species NOT cross a *horizontal* land bridge?
Can someone be penalized for an "unlawful" act if no penalty is specified?
Aging parents with no investments
How to support a colleague who finds meetings extremely tiring?
Are there any other methods to apply to solving simultaneous equations?
Button changing it's text & action. Good or terrible?
Pokemon Turn Based battle (Python)
What to do when moving next to a bird sanctuary with a loosely-domesticated cat?
How to manage monthly salary
Why is the maximum length of OpenWrt’s root password 8 characters?
What do hard-Brexiteers want with respect to the Irish border?
How are circuits which use complex ICs normally simulated?
Are there incongruent pythagorean triangles with the same perimeter and same area?
Time travel alters history but people keep saying nothing's changed
Where to refill my bottle in India?
Higher cup-1 product of coboundaries is also a coboundary?
The 2019 Stack Overflow Developer Survey Results Are InPontrjagin square (Mosher and Tangora Question)The complement of a Cartesian product for characterizing the closed sets of a product spaceGroup cohomology: cup product for cyclic groupsCohomology ring of a direct sum via Poincare dualityDoes the cup product on de Rham cohomology induce a nondegenerate bilinear form?Reference Request: Equivariant cup product in singular cohomologyNotational issues with group cohomologyLinking number and cup productDoes $H^bullet(G, mathbbZ)$ have a coalgebra structure?singular cohomology and Poincaré duality
$begingroup$
In the cohomology or the group cohomology theory, suppose $mu_1$ and $mu_2$ are coboundaries of arbitrary dimensions,
$$
mu_1=delta eta_1
$$
$$
mu_2=delta eta_2
$$
where $eta_1$ and $eta_2$ are their lower dimensional split cochains.
Could we prove that the higher cup 1 product is also a coboundary?
$$
mu_1 cup_1 mu_2=(delta eta_1)cup_1 (delta eta_2)=delta(beta)?
$$
If so, how do we write this $beta$ explicitly?
Is a Higher cup-1 product of coboundaries also a coboundary?
general-topology algebraic-topology homology-cohomology group-cohomology simplicial-complex
asked Mar 23 at 15:55
annie heartannie heart
673721
$endgroup$
add a comment |
$begingroup$
In the cohomology or the group cohomology theory, suppose $mu_1$ and $mu_2$ are coboundaries of arbitrary dimensions,
$$
mu_1=delta eta_1
$$
$$
mu_2=delta eta_2
$$
where $eta_1$ and $eta_2$ are their lower dimensional split cochains.
Could we prove that the higher cup 1 product is also a coboundary?
$$
mu_1 cup_1 mu_2=(delta eta_1)cup_1 (delta eta_2)=delta(beta)?
$$
If so, how do we write this $beta$ explicitly?
Is a Higher cup-1 product of coboundaries also a coboundary?
general-topology algebraic-topology homology-cohomology group-cohomology simplicial-complex
asked Mar 23 at 15:55
annie heartannie heart
673721
$endgroup$
$begingroup$
See this post for higher cup product mathoverflow.net/questions/268181/…
$endgroup$
– annie heart
Mar 23 at 16:05
$begingroup$
I also ask a related question: mathoverflow.net/q/326155/106497 in Use of Steenrod's Higher Cup product and the graded-commutativity
$endgroup$
– annie heart
Mar 23 at 16:44
add a comment |
$begingroup$
In the cohomology or the group cohomology theory, suppose $mu_1$ and $mu_2$ are coboundaries of arbitrary dimensions,
$$
mu_1=delta eta_1
$$
$$
mu_2=delta eta_2
$$
where $eta_1$ and $eta_2$ are their lower dimensional split cochains.
Could we prove that the higher cup 1 product is also a coboundary?
$$
mu_1 cup_1 mu_2=(delta eta_1)cup_1 (delta eta_2)=delta(beta)?
$$
If so, how do we write this $beta$ explicitly?
Is a Higher cup-1 product of coboundaries also a coboundary?
general-topology algebraic-topology homology-cohomology group-cohomology simplicial-complex
asked Mar 23 at 15:55
annie heartannie heart
673721
$endgroup$
In the cohomology or the group cohomology theory, suppose $mu_1$ and $mu_2$ are coboundaries of arbitrary dimensions,
$$
mu_1=delta eta_1
$$
$$
mu_2=delta eta_2
$$
where $eta_1$ and $eta_2$ are their lower dimensional split cochains.
Could we prove that the higher cup 1 product is also a coboundary?
$$
mu_1 cup_1 mu_2=(delta eta_1)cup_1 (delta eta_2)=delta(beta)?
$$
If so, how do we write this $beta$ explicitly?
Is a Higher cup-1 product of coboundaries also a coboundary?
general-topology algebraic-topology homology-cohomology group-cohomology simplicial-complex
general-topology algebraic-topology homology-cohomology group-cohomology simplicial-complex
asked Mar 23 at 15:55
annie heartannie heart
673721
asked Mar 23 at 15:55
annie heartannie heart
673721
asked Mar 23 at 15:55
annie heartannie heart
673721
asked Mar 23 at 15:55
annie heartannie heart
673721
asked Mar 23 at 15:55
annie heartannie heart
673721
673721
$begingroup$
See this post for higher cup product mathoverflow.net/questions/268181/…
$endgroup$
– annie heart
Mar 23 at 16:05
$begingroup$
I also ask a related question: mathoverflow.net/q/326155/106497 in Use of Steenrod's Higher Cup product and the graded-commutativity
$endgroup$
– annie heart
Mar 23 at 16:44
add a comment |
$begingroup$
See this post for higher cup product mathoverflow.net/questions/268181/…
$endgroup$
– annie heart
Mar 23 at 16:05
$begingroup$
I also ask a related question: mathoverflow.net/q/326155/106497 in Use of Steenrod's Higher Cup product and the graded-commutativity
$endgroup$
– annie heart
Mar 23 at 16:44
$begingroup$
See this post for higher cup product mathoverflow.net/questions/268181/…
$endgroup$
– annie heart
Mar 23 at 16:05
$begingroup$
See this post for higher cup product mathoverflow.net/questions/268181/…
$endgroup$
– annie heart
Mar 23 at 16:05
$begingroup$
I also ask a related question: mathoverflow.net/q/326155/106497 in Use of Steenrod's Higher Cup product and the graded-commutativity
$endgroup$
– annie heart
Mar 23 at 16:44
$begingroup$
I also ask a related question: mathoverflow.net/q/326155/106497 in Use of Steenrod's Higher Cup product and the graded-commutativity
$endgroup$
– annie heart
Mar 23 at 16:44
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%2f3159473%2fhigher-cup-1-product-of-coboundaries-is-also-a-coboundary%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%2f3159473%2fhigher-cup-1-product-of-coboundaries-is-also-a-coboundary%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
$begingroup$
See this post for higher cup product mathoverflow.net/questions/268181/…
$endgroup$
– annie heart
Mar 23 at 16:05
$begingroup$
I also ask a related question: mathoverflow.net/q/326155/106497 in Use of Steenrod's Higher Cup product and the graded-commutativity
$endgroup$
– annie heart
Mar 23 at 16:44