Timeline for Definitions of Hilbert Bundles
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2016 at 4:02 | vote | accept | Thangachelli Debopritama | ||
| Apr 27, 2016 at 0:18 | answer | added | Nik Weaver | timeline score: 3 | |
| Apr 26, 2016 at 23:36 | comment | added | Qfwfq | @TanujD., Yes, coherent sheaves (and their possibly "infinite dimensional" cousins, quasicoherent sheaves) have sections, which form vector spaces. But I don't think looking directly into the algebraic geometry literature would be the most sensible path... Maybe there is something analogous to QC sheaves in the noncommutative geometry literature? | |
| Apr 26, 2016 at 22:30 | comment | added | მამუკა ჯიბლაძე | For example, there is a well known characterization of finitely generated projectives: a $k$-module $P$ is such iff the canonical map $P^*\otimes_kM\to\operatorname{Hom}_k(P,M)$ is an isomorphism for all modules $M$. I wonder if one gets a sensible notion of a Hilbert bundle by using appropriate duals and tensor products with this in the infinite-dimensional situation. | |
| Apr 26, 2016 at 22:27 | comment | added | Thangachelli Debopritama | @Qfwfq Are there any nice references exploring this aspect, viz. upper-semicontinuity of dimension? Is there a parallel notion of sections in this context? | |
| Apr 26, 2016 at 22:26 | comment | added | მამუკა ჯიბლაძე | @Qfwfq On the other hand coherent sheaves are to vector bundles as finitely presented modules are to finitely generated projective modules (in a sense, exactly so). From this point of view one might argue that correct analogs of vector bundles should somehow carry some properties related to projectivity. | |
| Apr 26, 2016 at 22:18 | comment | added | Qfwfq | Only slightly related but: in algebraic/holomorphic geometry you have coherent sheaves that are pretty much like vector bundles in which the dimension of fibers can jump (in an upper semi-continuous way, in this case), and they are as "natural" objects as bundles are. | |
| Apr 26, 2016 at 22:08 | history | edited | Thangachelli Debopritama | CC BY-SA 3.0 |
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| Apr 26, 2016 at 13:11 | history | edited | Thangachelli Debopritama | CC BY-SA 3.0 |
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| S Apr 26, 2016 at 10:11 | history | edited | Thangachelli Debopritama |
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| S Apr 26, 2016 at 10:11 | history | suggested | Amir Sagiv |
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| Apr 26, 2016 at 10:10 | review | Suggested edits | |||
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| Apr 26, 2016 at 9:44 | review | First posts | |||
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| Apr 26, 2016 at 9:41 | history | asked | Thangachelli Debopritama | CC BY-SA 3.0 |