diff -r d5caffd01b72 -r 61541264d4b3 text/blobdef.tex --- a/text/blobdef.tex Thu Aug 11 13:26:00 2011 -0700 +++ b/text/blobdef.tex Thu Aug 11 13:54:38 2011 -0700 @@ -156,7 +156,7 @@ \end{itemize} Combining these two operations can give rise to configurations of blobs whose complement in $X$ is not a manifold. -Thus will need to be more careful when speaking of a field $r$ on the complement of the blobs. +Thus we will need to be more careful when speaking of a field $r$ on the complement of the blobs. \begin{example} \label{sin1x-example} Consider the four subsets of $\Real^3$, @@ -208,7 +208,7 @@ %and the entire configuration should be compatible with some gluing decomposition of $X$. \begin{defn} \label{defn:configuration} -A configuration of $k$ blobs in $X$ is an ordered collection of $k$ subsets $\{B_1, \ldots B_k\}$ +A configuration of $k$ blobs in $X$ is an ordered collection of $k$ subsets $\{B_1, \ldots, B_k\}$ of $X$ such that there exists a gluing decomposition $M_0 \to \cdots \to M_m = X$ of $X$ and for each subset $B_i$ there is some $0 \leq l \leq m$ and some connected component $M_l'$ of $M_l$ which is a ball, so $B_i$ is the image of $M_l'$ in $X$. @@ -238,7 +238,7 @@ \label{defn:blob-diagram} A $k$-blob diagram on $X$ consists of \begin{itemize} -\item a configuration $\{B_1, \ldots B_k\}$ of $k$ blobs in $X$, +\item a configuration $\{B_1, \ldots, B_k\}$ of $k$ blobs in $X$, \item and a field $r \in \cF(X)$ which is splittable along some gluing decomposition compatible with that configuration, \end{itemize} such that