Timeline for Homotopy equivalence of $K$-theory and $G$-theory
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Jul 21, 2019 at 21:40 | comment | added | user127776 | In fact the only thing I need is the existence of a retraction that maps all rank zero coherent sheaves to 0. | |
| Jul 21, 2019 at 21:37 | comment | added | user127776 | I need this because of the rank filtration. I want to analyze the homology classes coming from rank filtration so for a homology class it is important for me to find a representative of this cycle with minimal vertex rank. I was trying to understand the relation of this type of rank filtration and the Adams filtration (They seem to be strangely related) this is required in the process that by pull back to an open subset this filtration is preserved. | |
| Jul 21, 2019 at 21:32 | comment | added | Denis Nardin | I doubt you can find an explicit retraction. I don't know if there is a constructive proof of Quillen's theorem A (the one I know is really not constructive) Can you elaborate on why do you need such a thing? As I said, the vertices of $Q\mathcal{C}$ contain basically no information at all. | |
| Jul 21, 2019 at 21:13 | history | edited | user127776 | CC BY-SA 4.0 |
added 1341 characters in body
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| Jul 21, 2019 at 20:01 | comment | added | Denis Nardin | Note that the space $Q(\mathrm{Vect}(X))$ is connected, so all its vertices are essentially undistinguishable for all homotopy-theoretic purposes. I suspect you are interested on the behaviour on $\pi_1$ (i.e. $K_0$) instead | |
| Jul 21, 2019 at 16:59 | history | asked | user127776 | CC BY-SA 4.0 |