1830 Let $C(S)$ denote the cone of $S$, a marked 2-ball (Figure \ref{feb21d}). |
1830 Let $C(S)$ denote the cone of $S$, a marked 2-ball (Figure \ref{feb21d}). |
1831 \nn{I need to make up my mind whether marked things are always labeled too. |
1831 \nn{I need to make up my mind whether marked things are always labeled too. |
1832 For the time being, let's say they are.} |
1832 For the time being, let's say they are.} |
1833 A 1-marked $k$-ball is anything homeomorphic to $B^j \times C(S)$, $0\le j\le n-2$, |
1833 A 1-marked $k$-ball is anything homeomorphic to $B^j \times C(S)$, $0\le j\le n-2$, |
1834 where $B^j$ is the standard $j$-ball. |
1834 where $B^j$ is the standard $j$-ball. |
1835 A 1-marked $k$-balls can be decomposed in various ways into smaller balls, which are either |
1835 A 1-marked $k$-ball can be decomposed in various ways into smaller balls, which are either |
1836 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} |
1836 (a) smaller 1-marked $k$-balls, (b) 0-marked $k$-balls, or (c) plain $k$-balls. |
|
1837 (See Figure xxxx.) |
1837 We now proceed as in the above module definitions. |
1838 We now proceed as in the above module definitions. |
1838 |
1839 |
1839 \begin{figure}[!ht] |
1840 \begin{figure}[!ht] |
1840 $$ |
1841 $$ |
1841 \begin{tikzpicture}[baseline,line width = 2pt] |
1842 \begin{tikzpicture}[baseline,line width = 2pt] |