Knot invariant in arbitrary 3-manifold
$begingroup$
In famous Witten's paper "Quantum Field Theory and Jones Polynomial", Witten proposed
$int DA exp{iL} prod_{k=1}^{r} W_{R_t} (C_i)$
as the knot invariant in ARBITRARY 3-manifold.
($L$ is a Langlangian of Chern-Simons 3-form, and the integral is Feynman path integral of gauge transformation.)
After Witten's paper, Turaev formulated Witten's idia as the quantum invariants. But Quantum invariants are defined only for knots in $S^3$.
Does anyone know "Quantum invariants in arbitrary 3-manifold"?
Cf
1.Witten's paper and Turaev's paper
https://projecteuclid.org/download/pdf_1/euclid.cmp/1104178138
http://mathlab.snu.ac.kr/~top/quantum/article/Reshetikhin01.pdf
2.knot theory in $RP^3$
https://arxiv.org/pdf/math/0312205.pdf
3.related question
Unknown Witten-Reshetikhin-Turaev (WRT) Invariants for a 3 Manifold
Knot theory on arbitrary manifolds.
knot-theory
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
$endgroup$
add a comment |
$begingroup$
In famous Witten's paper "Quantum Field Theory and Jones Polynomial", Witten proposed
$int DA exp{iL} prod_{k=1}^{r} W_{R_t} (C_i)$
as the knot invariant in ARBITRARY 3-manifold.
($L$ is a Langlangian of Chern-Simons 3-form, and the integral is Feynman path integral of gauge transformation.)
After Witten's paper, Turaev formulated Witten's idia as the quantum invariants. But Quantum invariants are defined only for knots in $S^3$.
Does anyone know "Quantum invariants in arbitrary 3-manifold"?
Cf
1.Witten's paper and Turaev's paper
https://projecteuclid.org/download/pdf_1/euclid.cmp/1104178138
http://mathlab.snu.ac.kr/~top/quantum/article/Reshetikhin01.pdf
2.knot theory in $RP^3$
https://arxiv.org/pdf/math/0312205.pdf
3.related question
Unknown Witten-Reshetikhin-Turaev (WRT) Invariants for a 3 Manifold
Knot theory on arbitrary manifolds.
knot-theory
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
$endgroup$
add a comment |
$begingroup$
In famous Witten's paper "Quantum Field Theory and Jones Polynomial", Witten proposed
$int DA exp{iL} prod_{k=1}^{r} W_{R_t} (C_i)$
as the knot invariant in ARBITRARY 3-manifold.
($L$ is a Langlangian of Chern-Simons 3-form, and the integral is Feynman path integral of gauge transformation.)
After Witten's paper, Turaev formulated Witten's idia as the quantum invariants. But Quantum invariants are defined only for knots in $S^3$.
Does anyone know "Quantum invariants in arbitrary 3-manifold"?
Cf
1.Witten's paper and Turaev's paper
https://projecteuclid.org/download/pdf_1/euclid.cmp/1104178138
http://mathlab.snu.ac.kr/~top/quantum/article/Reshetikhin01.pdf
2.knot theory in $RP^3$
https://arxiv.org/pdf/math/0312205.pdf
3.related question
Unknown Witten-Reshetikhin-Turaev (WRT) Invariants for a 3 Manifold
Knot theory on arbitrary manifolds.
knot-theory
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
$endgroup$
In famous Witten's paper "Quantum Field Theory and Jones Polynomial", Witten proposed
$int DA exp{iL} prod_{k=1}^{r} W_{R_t} (C_i)$
as the knot invariant in ARBITRARY 3-manifold.
($L$ is a Langlangian of Chern-Simons 3-form, and the integral is Feynman path integral of gauge transformation.)
After Witten's paper, Turaev formulated Witten's idia as the quantum invariants. But Quantum invariants are defined only for knots in $S^3$.
Does anyone know "Quantum invariants in arbitrary 3-manifold"?
Cf
1.Witten's paper and Turaev's paper
https://projecteuclid.org/download/pdf_1/euclid.cmp/1104178138
http://mathlab.snu.ac.kr/~top/quantum/article/Reshetikhin01.pdf
2.knot theory in $RP^3$
https://arxiv.org/pdf/math/0312205.pdf
3.related question
Unknown Witten-Reshetikhin-Turaev (WRT) Invariants for a 3 Manifold
Knot theory on arbitrary manifolds.
knot-theory
knot-theory
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
asked Dec 15 '18 at 13:44
this_is_a_bananathis_is_a_banana
855
855
add a comment |
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%2f3041508%2fknot-invariant-in-arbitrary-3-manifold%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%2f3041508%2fknot-invariant-in-arbitrary-3-manifold%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
