Timeline for Topological K-theory of Riemann surface
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2022 at 15:08 | comment | added | user479269 | Just an FYI: For general complex projective manifolds, Section 5.1 in The integral Hodge conjecture for two-dimensional Calabi-Yau categories might be helpful (which refers to the fancy paper Topological K-theory of complex noncommutative spaces). | |
| Mar 8, 2022 at 20:36 | history | edited | user39380 | CC BY-SA 4.0 |
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| Mar 8, 2022 at 20:24 | vote | accept | CommunityBot | ||
| Mar 8, 2022 at 20:23 | comment | added | user39380 | @DanRamras Yes, thanks! I think on $K^0_{top}(X)$, and vector bundles $E,F$, we can define $\langle E,F\rangle=\chi(E^\vee\otimes F)$, and the definition can be extended to complexes on vector bundles hence $K_{top}^0(X)$, and I am not quite sure if the pairing naturally extend to $K^1_{top}(X)$.. (The motivation was to understand the topological $K$-theory in the case of curves, I had (carelessly )thought such thing exist as an analogue of Poincare duality) | |
| Mar 8, 2022 at 20:14 | history | edited | user39380 | CC BY-SA 4.0 |
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| Mar 7, 2022 at 15:40 | comment | added | Dan Ramras | It would be helpful to explain exactly what is meant by the Euler pairing. I see it mentioned in your other question, with different notation. mathoverflow.net/questions/417368/… | |
| Mar 7, 2022 at 15:17 | answer | added | Dan Ramras | timeline score: 4 | |
| Mar 5, 2022 at 23:16 | comment | added | kiran | There's a map K(Z,1)~U(1)--> U and I'd imagine that induces an isomorphism betwen H^1 and K^1 in this case. At the very least it works for n=1 (and n=0...) | |
| Mar 5, 2022 at 22:46 | history | asked | user39380 | CC BY-SA 4.0 |