Lelouch
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Registered User
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Studying physics, but very interested in geometry and topology.
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May 16 |
awarded | ● Commentator |
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May 16 |
comment |
How to characterize this particular kind of bundle? Is there convenient invariants like Chern numbers (invariants expressed as integral of local quantities) that could be used to characterize a bundle (vector of principal) over an odd dimensional manifold? |
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May 16 |
comment |
How to characterize this particular kind of bundle? So a natural principal bundle on $M_4$ is just the one by composing two projection of $P$ onto $M_4$, with fiber loosely speaking $G \times S^1$. And when $P$ over $M_5$ is trivial, the induced bundle $P$ over $M_4$ will not be trivial if $M_5$ is a non-trivial $S^1$-bundle over $M_4$. |
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May 15 |
revised |
How to characterize this particular kind of bundle? Delete irrelevant questions; edited title |
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May 15 |
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How to characterize this particular kind of bundle? @Daniele Zuddas: Ok. Let me edit the question. Thanks. |
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May 15 |
revised |
How to characterize this particular kind of bundle? added 450 characters in body |
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May 15 |
asked | How to characterize this particular kind of bundle? |
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May 9 |
awarded | ● Enthusiast |
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May 2 |
awarded | ● Teacher |
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May 1 |
answered | On Dimension of Instanton Moduli Space |
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Apr 20 |
revised |
On Dimension of Instanton Moduli Space New calculation result performed, but question remained |
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Apr 19 |
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On Dimension of Instanton Moduli Space @Liviu Nicolaescu: Thanks, I definitely will look at the paper, though maybe I should first try to complete the brute force expansion of curvature tensors. |
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Apr 19 |
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How to understand Chern-Simons action Thanks for the explanation. To me there is a hierarchy between odd and even dimension: even dimensional characteristic classes are much easier to understand/write down than the secondary ones, while the latter needs a "reference connection $\nabla_0$" to be well-defined. I can understand that since there is no elementary gauge invariant odd-forms (all we can use is $F_{\mu\nu}$ with traces) on the base manifold. It seems mathematical notion "bundle" care/like even dimensional cohomology more than odd ones. Is there another notion that could care more about odd-dimensional cohomology? |
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Apr 19 |
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How to understand Chern-Simons action Thanks~Actually I came across Freed's notes some time ago, but I stopped reading as I found myself further and further away from "real physics", in some sense:).But no doubt the 2 are very good notes and I shall go back to them. |
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Apr 18 |
revised |
How to understand Chern-Simons action deleted 38 characters in body |
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Apr 18 |
asked | On Dimension of Instanton Moduli Space |
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Apr 18 |
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How to understand Chern-Simons action Though I do not fully understand the categorical generalization you provided, I do now understand why higher, say 5-dimensional CS theory is much less studied in physics community: the action is difficult to write down with enough generality. But now 5d gauge theory is attracting more attentions, and I see in physics papers we are still using the most simple CS-action. Maybe we should write down a sensible 5d Chern-Simons(-like) theory, with some obvious ("easy" but general enough) modification to 3d one. Does anything like this exists already? Thanks. |
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Apr 18 |
asked | How to understand Chern-Simons action |
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Apr 18 |
comment |
the existence of (almost) contact (metric) structure Thank you for your answer! Let me make sure I understand some points you made: (1) So any compact+oriented 3-manifold $\Rightarrow$ Open-book decomposition $\Rightarrow$ contact structure, without any requirement of vanishing the 3rd S-W class? Actually I am mainly interested in $d= 5$ and almost contact structure, as it relates to some physics developing lately. But indeed I can't find much about them through googling. |
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Apr 18 |
revised |
Behavior of Reeb vector field (or almost contact 1-form), and “Contact instanton” added 176 characters in body |
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Apr 18 |
asked | Behavior of Reeb vector field (or almost contact 1-form), and “Contact instanton” |
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Apr 11 |
revised |
the existence of (almost) contact (metric) structure corrected author's name |
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Apr 11 |
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the existence of (almost) contact (metric) structure Thanks for you answer and sorry to misspell author's name. I'll edit it. |
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Apr 10 |
awarded | ● Editor |
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Apr 10 |
revised |
the existence of (almost) contact (metric) structure added 11 characters in body |
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Apr 10 |
asked | the existence of (almost) contact (metric) structure |
