133 Up to homotopy, $S^1$ acts by $j$-fold rotation on $\Sigma^j(S^1) \simeq S^1/j$.

   133 Up to homotopy, $S^1$ acts by $j$-fold rotation on $\Sigma^j(S^1) \simeq S^1/j$.

   134 If $k = \z$, $\Sigma^j(S^1)$ contributes the homology of an infinite lens space: $\z$ in degree

   134 If $k = \z$, $\Sigma^j(S^1)$ contributes the homology of an infinite lens space: $\z$ in degree

   135 0, $\z/j \z$ in odd degrees, and 0 in positive even degrees.

   135 0, $\z/j \z$ in odd degrees, and 0 in positive even degrees.

   136 The point $\Sigma^0(S^1)$ contributes the homology of $BS^1$ which is $\z$ in even 

   136 The point $\Sigma^0(S^1)$ contributes the homology of $BS^1$ which is $\z$ in even 

   137 degrees and 0 in odd degrees.

   137 degrees and 0 in odd degrees.

   139 

   139 

   140 \medskip

   140 \medskip

   141 

   141 

   142 Next we consider the case $C = k[t_1, \ldots, t_m]$, commutative polynomials in $m$ variables.

   142 Next we consider the case $C = k[t_1, \ldots, t_m]$, commutative polynomials in $m$ variables.

   143 Let $\Sigma_m^\infty(M)$ be the $m$-colored infinite symmetric power of $M$, that is, configurations

   143 Let $\Sigma_m^\infty(M)$ be the $m$-colored infinite symmetric power of $M$, that is, configurations

   187 

   187 

   188 Still to do:

   188 Still to do:

   189 \begin{itemize}

   189 \begin{itemize}

   190 \item compare the topological computation for truncated polynomial algebra with \cite{MR1600246}

   190 \item compare the topological computation for truncated polynomial algebra with \cite{MR1600246}

   191 \item multivariable truncated polynomial algebras (at least mention them)

   191 \item multivariable truncated polynomial algebras (at least mention them)

   194 \end{itemize}

   192 \end{itemize}

   195 

   193