# HG changeset patch # User Kevin Walker # Date 1277484504 25200 # Node ID 979fbe9a14e849689a86b215da7516596e6f37b3 # Parent 2a9c637182f096f1c43b3dfa3fd9281e682c7ed1 minor diff -r 2a9c637182f0 -r 979fbe9a14e8 text/ncat.tex --- a/text/ncat.tex Thu Jun 24 14:21:51 2010 -0400 +++ b/text/ncat.tex Fri Jun 25 09:48:24 2010 -0700 @@ -1832,8 +1832,9 @@ For the time being, let's say they are.} A 1-marked $k$-ball is anything homeomorphic to $B^j \times C(S)$, $0\le j\le n-2$, where $B^j$ is the standard $j$-ball. -A 1-marked $k$-balls can be decomposed in various ways into smaller balls, which are either -smaller 1-marked $k$-balls or the product of an unmarked ball with a marked interval. \todo{I'm confused by this last sentence. By `the product of an unmarked ball with a marked internal', you mean a 0-marked $k$-ball, right? If so, we should say it that way. Further, there are also just some entirely unmarked balls. -S} +A 1-marked $k$-ball can be decomposed in various ways into smaller balls, which are either +(a) smaller 1-marked $k$-balls, (b) 0-marked $k$-balls, or (c) plain $k$-balls. +(See Figure xxxx.) We now proceed as in the above module definitions. \begin{figure}[!ht]