Timeline for Direct proof of the equivalence of symmetric monoidal $K$-theory and exact sequence $K$-theory?
Current License: CC BY-SA 3.0
11 events
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| Mar 17, 2018 at 19:50 | comment | added | user20948 | Lurie has a lecture note rewriting Waldhausen's proof in terms of $\infty$-categories, although he losses some generalities of Waldhausen's. | |
| Mar 13, 2018 at 21:29 | comment | added | Tim Campion | A reference I should have checked before -- Waldhausen, section 1.8, proves this, using the models that I have in mind. I will have to unpack his proof a bit. | |
| Mar 13, 2018 at 18:30 | comment | added | Tim Campion | Hmm... Now I'm confused. Theorem 1 in that paper is basically what I'm looking for: it says that $S_\bullet C \to BC$ is a homology isomorpshism -- except that there are conditions on the coefficients (if it was an integral homology isomorphism, it would be a homotopy equivalence since these are H-spaces). But the comparison of K-theories is supposed to be an actual homotopy equivalence... | |
| Mar 13, 2018 at 12:38 | comment | added | K.J. Moi | Quillen's paper "Characteristic classes of representations" (link below) deals with this question from a cohomological perspective. Check out theorem 2'. I hope you have access via the link to Springer: link.springer.com/content/pdf/10.1007/BFb0080002.pdf | |
| Mar 13, 2018 at 12:24 | history | edited | YCor |
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| Mar 13, 2018 at 12:16 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Mar 13, 2018 at 1:10 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Mar 12, 2018 at 23:49 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Mar 12, 2018 at 23:33 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Mar 12, 2018 at 23:15 | history | edited | Tim Campion | CC BY-SA 3.0 |
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| Mar 12, 2018 at 23:08 | history | asked | Tim Campion | CC BY-SA 3.0 |