Timeline for Karoubi versus Kasparov K-theory
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 13, 2013 at 5:40 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 1 characters in body
|
| May 22, 2013 at 12:36 | comment | added | Liviu Nicolaescu | My experience with index theory is that it is multi-faceted: the aspects of this theory one observes depend on the particular line of investigation. | |
| May 21, 2013 at 16:06 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 689 characters in body; added 82 characters in body; added 43 characters in body
|
| May 21, 2013 at 16:01 | comment | added | Johannes Ebert | Still, it feels too complicated. What I imagined is that to a Karoubi triple $(E, \eta_0,\eta_1)$, one can associate a Kasparov element $(H,F)$, where $H$ is the space of sections in a \emph{finite-dimensional} graded $Cl^{q,p}$-vector bundle and $F$ some operator. Or is this too naive and there exists an obstruction against this? | |
| May 21, 2013 at 14:59 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 3 characters in body
|
| May 21, 2013 at 14:02 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 37 characters in body
|
| May 21, 2013 at 13:25 | history | edited | Liviu Nicolaescu | CC BY-SA 3.0 |
added 3359 characters in body; deleted 10 characters in body
|
| May 21, 2013 at 11:25 | comment | added | Liviu Nicolaescu | In the old paper I describe an explicit map $K^{p,q}(X)\to [X,\mathscr{FL}^{p,q}]$. The symplectic reduction is a sort of inverse of this map. Because of space I will give the details as an update to my post. | |
| May 21, 2013 at 10:36 | comment | added | Johannes Ebert | Alternatively, I could rephrase my question: How do I make $K^{p,q}(X) \to [X; \mathcal{F}^{p,q}]$ explicit (in this direction; otherwise it is useless in the context where this question arose) | |
| May 21, 2013 at 10:35 | comment | added | Johannes Ebert | Mapping from the space $\mathcal{F}^{p,q}$ to $KK$-theory is much simpler. First of all, it should be the space of $Cl^{p,q+1}$-antilinear Fredholms. When you consider the last basis vector as a grading, you get a graded Hilbert space, with a graded $Cl^{p,q}$-action. The operator $F$ anticommutes with that action, hence it defines a Kasparov module for $KK(Cl^{p,q};R)$. | |
| May 21, 2013 at 10:26 | comment | added | Johannes Ebert | This is not what I would call an explicit map. | |
| May 21, 2013 at 10:04 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |