Timeline for K-theory of non-compact spaces
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2016 at 13:03 | vote | accept | Thomas Rot | ||
| Mar 26, 2016 at 21:47 | answer | added | Dmitri Pavlov | timeline score: 4 | |
| Mar 26, 2016 at 2:46 | answer | added | Mike-Doherty | timeline score: 8 | |
| Mar 26, 2016 at 2:45 | comment | added | Anton Fetisov | @DenisNardin , I don't think they are equivalent. I suppose def. 2 uses a limit of sets rather than a homotopy colimit of spaces (since you can't define it without considering Fredholm space like in def. 3). Thus 2 and 3 are related by the Milnor exact sequence. | |
| Mar 25, 2016 at 14:22 | history | edited | ThiKu | CC BY-SA 3.0 |
minor typos
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| Mar 25, 2016 at 13:30 | history | edited | Thomas Rot | CC BY-SA 3.0 |
deleted 7 characters in body
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| Mar 25, 2016 at 13:27 | answer | added | Fabio | timeline score: 8 | |
| Mar 25, 2016 at 12:20 | comment | added | Paul Siegel | Atiyah probably used definition 1 because he wanted a Thom isomorphism theorem in K-theory for vector bundles over compact manifolds. Comparing with the proof of the Thom isomorphism theorem in cohomology, it is not unreasonable to impose a compact support condition, at least in the fiber direction. | |
| Mar 25, 2016 at 12:00 | comment | added | Denis Nardin | I've never seen 1., but 2. and 3. are equivalent (that's because every CW is the homotopy colimit of its finite subcomplexes). In general a cohomology theory is best studied on (spaces homotopy equivalent to) finite CW complexes and extended in that way to general spaces, so that it satisfies the Eilenberg-Steenrod axioms. | |
| Mar 25, 2016 at 11:36 | history | asked | Thomas Rot | CC BY-SA 3.0 |