closes #127

Author: ecpeterson

quillen.tex

@@ -1021,7 +1021,7 @@ \section{The complex bordism ring}\label{CalculationOfMUStarSection}
 \begin{proof}[{Proof of \Cref{CGenerationForFiniteCplx}}]
 We can immediately reduce the claim in two ways.  First, it is true if and only if it is also true for reduced cohomology.  Second, we are free to restrict attention just to \(MU^{2*}(X)\), since we can handle the odd-degree parts of \(MU^*(X)\) by suspending \(X\) once.  Defining \[R^{2*} := C \cdot \sum_{q > 0} MU^{2q}(X),\] we can thus focus on the claim \[\widetilde{MU}^{2*}(X) \stackrel{?}{=} R^{2*} = C \cdot \sum_{q > 0} MU^{2q}(X).\]  Noting that the claim is trivially true for all positive values of \(*\), we will show this by working \(p\)--locally and inducting on the value of ``\(-*\)''.
 
-Suppose that \[R^{-2j}_{(p)} = \widetilde{MU}^{-2j}(X)_{(p)}\] for \(j < q\) and consider \(x \in \widetilde{MU}^{-2q}(X)_{(p)}\).  Then, for \(m \gg 0\), we have
+Suppose that \[R^{-2j}_{(p)} = \widetilde{MU}^{-2j}(X)_{(p)}\] for \(j < q\) and consider \(x \in \widetilde{MU}^{-2q}(X)\).  Then, for \(m \gg 0\), we have
 \begin{align*}
 w^m P^{C_p}(x) & = \sum_{|\alpha| \le m-q} w^{m-q - |\alpha|} a(t)^\alpha s_\alpha x \\
 & = w^{m-q} x + \sum_{\substack{|\alpha| \le m-q \\ \alpha \ne 0}} w^{m-q - |\alpha|} a(t)^\alpha s_\alpha x.