bio | website | |
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location | Philadelphia | |
age | 27 | |
visits | member for | 4 years, 1 month |
seen | 18 hours ago | |
stats | profile views | 1,012 |
grad student at upenn.
Mar 30 |
comment |
Atiyah classes of holomorphic vector bundles with trivial Chern classes
@PavelSafronov Err, now I'm confused. Topologically we have $\mathcal (O(-1)\otimes \mathcal O(-1))\oplus \mathbb C = \mathcal O(-1) \oplus \mathcal O(-1)$. So topologically, $\mathcal O(1) \oplus \mathcal O(-1) = \mathbb C^2$ is trivial and so admits a flat connection. |
Mar 30 |
comment |
Atiyah classes of holomorphic vector bundles with trivial Chern classes
@PavelSafronov Thanks. Also I just realized since $\pi_1(\mathbb P^1) = 0$ the only flat rank 2 vector bundle is trivial. |
Mar 30 |
accepted | Atiyah classes of holomorphic vector bundles with trivial Chern classes |
Mar 30 |
comment |
Atiyah classes of holomorphic vector bundles with trivial Chern classes
Thanks for the answer! Do you happen to have a reference for the theorem of Weil? Also, do you know offhand if $\mathcal{O}_{\mathbb{P}^1}(p)\oplus \mathcal{O}_{\mathbb{P}^1}(-p)$ admits a flat connection? |
Mar 30 |
revised |
Atiyah classes of holomorphic vector bundles with trivial Chern classes
edited title |
Mar 30 |
asked | Atiyah classes of holomorphic vector bundles with trivial Chern classes |
Mar 26 |
comment |
Geometric Quantization
@SanathDevalapurkar Sorry, what I meant is that for a general configuration space there is no known canonical way to quantize it. The point is that geometric quantization gives one method to quantize a space that satisfies certain conditions. That this is a "correct" approach comes down to it satisfying certain axioms a quantization should have and agreeing in the simple cases with what physicists expect (e.g. on $\mathbb R^n$ or $S^2$). |
Mar 26 |
comment |
Geometric Quantization
@SanathDevalapurkar this is no general method of quantization. I would check out these mathoverflow posts mathoverflow.net/questions/6200/what-is-quantization mathoverflow.net/questions/8606/… |
Mar 26 |
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Geometric Quantization
@SanathDevalapurkar are you able to see why if you start with $X = \mathbb R^n$ you get the usual quantization of first year quantum courses? |
Mar 14 |
awarded | Yearling |
Jan 21 |
awarded | Notable Question |
Jan 13 |
awarded | Popular Question |
Jan 12 |
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Hilbert's syzygy theorem in the analytic setting
@user76758 thanks. maybe you should make your comment an answer. also, do you have good references for these statements? thanks. |
Jan 9 |
asked | Hilbert's syzygy theorem in the analytic setting |
Aug 26 |
awarded | Tag Editor |
Aug 26 |
revised |
lie-groups wiki excerpt
added 3 characters in body |
Aug 26 |
suggested | suggested edit on lie-groups tag wiki excerpt |
Jul 24 |
awarded | Nice Question |
Jun 14 |
accepted | Are all representations of $G\times H$ induced from representations of $G$ and $H$? |
Jun 11 |
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Are all representations of $G\times H$ induced from representations of $G$ and $H$?
Thanks for the nice counterexample! |