Closed solov-t closed 1 week ago
Also I think Fabian used a normalized version of C^simp, which maybe is worth pointing out but idk.
Thanks for the feedback!
I'm pretty sure the tensor product should be taken over Z because C^simp, as we defined it, has coefficients in Z and is thus not an R-module. But you could also define C^simp with coefficients in R instead of Z, and then the tensor product should indeed be taken over R (and $C\otimes_Z C^simp(X)$ is the same complex as $C\otimes_RC^simp(X,R)$).
However, you are totally right about that C^simp should be normalized (I somehow forgot that $\Delta^n$ contains degenerate simplices lol) and I believe Dold-Kan only works that way.
I'll try to fix this together with tomorrow's lecture, but I'll still keep the issue as there will undoubtedly be more errors like this.
Oh yes this makes perfect sense! Somehow I was tired and didn't try to actually compute this haha
Hello Florian,
On the K-theory notes, example I.15 (e) is it supposed to be tensor product over $R$? And also on the definition of C^simp, etc, etc... I think Fabian said over Z as well, but I'm a bit confused.
(Great notes btw!)