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824 \begin{example}[The bordism $n$-category, ordinary version] |
824 \begin{example}[The bordism $n$-category, ordinary version] |
825 \label{ex:bord-cat} |
825 \label{ex:bord-cat} |
826 \rm |
826 \rm |
827 \label{ex:bordism-category} |
827 \label{ex:bordism-category} |
828 For a $k$-ball $X$, $k<n$, define $\Bord^n(X)$ to be the set of all $k$-dimensional PL |
828 For a $k$-ball $X$, $k<n$, define $\Bord^n(X)$ to be the set of all $k$-dimensional PL |
829 submanifolds $W$ of $X\times \Real^\infty$ such that $\bd W$ is |
829 submanifolds $W$ of $X\times \Real^\infty$ such that $\bd W = W \cap \bd X \times \Real^\infty$. |
830 contained in $\bd X \times \Real^\infty$. |
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831 For an $n$-ball $X$ define $\Bord^n(X)$ to be homeomorphism classes (rel boundary) of such $n$-dimensional submanifolds; |
830 For an $n$-ball $X$ define $\Bord^n(X)$ to be homeomorphism classes (rel boundary) of such $n$-dimensional submanifolds; |
832 we identify $W$ and $W'$ if $\bd W = \bd W'$ and there is a homeomorphism |
831 we identify $W$ and $W'$ if $\bd W = \bd W'$ and there is a homeomorphism |
833 $W \to W'$ which restricts to the identity on the boundary. |
832 $W \to W'$ which restricts to the identity on the boundary. |
834 \end{example} |
833 \end{example} |
835 |
834 |