diff -r 5234b7329042 -r 75f5c197a0d4 text/comm_alg.tex --- a/text/comm_alg.tex Sun Nov 01 20:29:33 2009 +0000 +++ b/text/comm_alg.tex Sun Nov 01 20:29:41 2009 +0000 @@ -112,8 +112,8 @@ \nn{probably should put a more precise statement about cyclic homology and $S^1$ actions in the Hochschild section} Let us check this directly. -According to \nn{Loday, 3.2.2}, $HH_i(k[t]) \cong k[t]$ for $i=0,1$ and is zero for $i\ge 2$. -\nn{say something about $t$-degree? is this in [Loday]?} +According to \cite[3.2.2]{MR1600246}, $HH_i(k[t]) \cong k[t]$ for $i=0,1$ and is zero for $i\ge 2$. +\nn{say something about $t$-degree? is this in Loday?} We can define a flow on $\Sigma^j(S^1)$ by having the points repel each other. The fixed points of this flow are the equally spaced configurations. @@ -135,7 +135,7 @@ 0, $\z/j \z$ in odd degrees, and 0 in positive even degrees. The point $\Sigma^0(S^1)$ contributes the homology of $BS^1$ which is $\z$ in even degrees and 0 in odd degrees. -This agrees with the calculation in \nn{Loday, 3.1.7}. +This agrees with the calculation in \cite[3.1.7]{MR1600246}. \medskip @@ -150,7 +150,7 @@ $\bc_*(M, k[t_1, \ldots, t_m])$ is homotopy equivalent to $C_*(\Sigma_m^\infty(M), k)$. \end{prop} -According to \nn{Loday, 3.2.2}, +According to \cite[3.2.2]{MR1600246}, \[ HH_n(k[t_1, \ldots, t_m]) \cong \Lambda^n(k^m) \otimes k[t_1, \ldots, t_m] . \] @@ -186,7 +186,7 @@ Still to do: \begin{itemize} -\item compare the topological computation for truncated polynomial algebra with [Loday] +\item compare the topological computation for truncated polynomial algebra with \cite{MR1600246} \item multivariable truncated polynomial algebras (at least mention them) \item ideally, say something more about higher hochschild homology (maybe sketch idea for proof of equivalence) \end{itemize}