diff -r 07c18e2abd8f -r 4d0ca2fc4f2b text/a_inf_blob.tex --- a/text/a_inf_blob.tex Thu Jul 22 15:35:26 2010 -0600 +++ b/text/a_inf_blob.tex Thu Jul 22 16:16:58 2010 -0600 @@ -69,7 +69,8 @@ Let $G_*\sub \bc_*(Y\times F;C)$ be the subcomplex generated by blob diagrams $a$ such that there exists a decomposition $K$ of $Y$ such that $a$ splits along $K\times F$. -It follows from Proposition \ref{thm:small-blobs} that $\bc_*(Y\times F; C)$ is homotopic to a subcomplex of $G_*$. +It follows from Proposition \ref{thm:small-blobs} that $\bc_*(Y\times F; C)$ +is homotopic to a subcomplex of $G_*$. (If the blobs of $a$ are small with respect to a sufficiently fine cover then their projections to $Y$ are contained in some disjoint union of balls.) Note that the image of $\psi$ is equal to $G_*$. @@ -95,7 +96,8 @@ \end{lemma} \begin{proof} -We will prove acyclicity in the first couple of degrees, and \nn{in this draft, at least} +We will prove acyclicity in the first couple of degrees, and +%\nn{in this draft, at least} leave the general case to the reader. Let $K$ and $K'$ be two decompositions (0-simplices) of $Y$ compatible with $a$.