835 to be the dual Hilbert space $A(X\times F; c)$. |
835 to be the dual Hilbert space $A(X\times F; c)$. |
836 (See \S\ref{sec:constructing-a-tqft}.) |
836 (See \S\ref{sec:constructing-a-tqft}.) |
837 \end{example} |
837 \end{example} |
838 |
838 |
839 |
839 |
840 \begin{example}[te bordism $n$-category of $d$-manifolds, ordinary version] |
840 \begin{example}[The bordism $n$-category of $d$-manifolds, ordinary version] |
841 \label{ex:bord-cat} |
841 \label{ex:bord-cat} |
842 \rm |
842 \rm |
843 \label{ex:bordism-category} |
843 \label{ex:bordism-category} |
844 For a $k$-ball $X$, $k<n$, define $\Bord^{n,d}(X)$ to be the set of all $(d{-}n{+}k)$-dimensional PL |
844 For a $k$-ball $X$, $k<n$, define $\Bord^{n,d}(X)$ to be the set of all $(d{-}n{+}k)$-dimensional PL |
845 submanifolds $W$ of $X\times \Real^\infty$ such that $\bd W = W \cap \bd X \times \Real^\infty$. |
845 submanifolds $W$ of $X\times \Real^\infty$ such that $\bd W = W \cap \bd X \times \Real^\infty$. |
910 is not the $A_\infty$ $n$-category $\pi^\infty_{\leq n}(T)$. |
910 is not the $A_\infty$ $n$-category $\pi^\infty_{\leq n}(T)$. |
911 It's easy to see that with $n=0$, the corresponding system of fields is just |
911 It's easy to see that with $n=0$, the corresponding system of fields is just |
912 linear combinations of connected components of $T$, and the local relations are trivial. |
912 linear combinations of connected components of $T$, and the local relations are trivial. |
913 There's no way for the blob complex to magically recover all the data of $\pi^\infty_{\leq 0}(T) \iso C_* T$. |
913 There's no way for the blob complex to magically recover all the data of $\pi^\infty_{\leq 0}(T) \iso C_* T$. |
914 |
914 |
915 \begin{example}[te bordism $n$-category of $d$-manifolds, $A_\infty$ version] |
915 \begin{example}[The bordism $n$-category of $d$-manifolds, $A_\infty$ version] |
916 \rm |
916 \rm |
917 \label{ex:bordism-category-ainf} |
917 \label{ex:bordism-category-ainf} |
918 As in Example \ref{ex:bord-cat}, for $X$ a $k$-ball, $k<n$, we define $\Bord^{n,d}_\infty(X)$ |
918 As in Example \ref{ex:bord-cat}, for $X$ a $k$-ball, $k<n$, we define $\Bord^{n,d}_\infty(X)$ |
919 to be the set of all $(d{-}n{+}k)$-dimensional |
919 to be the set of all $(d{-}n{+}k)$-dimensional |
920 submanifolds $W$ of $X\times \Real^\infty$ such that $\bd W = W \cap \bd X \times \Real^\infty$. |
920 submanifolds $W$ of $X\times \Real^\infty$ such that $\bd W = W \cap \bd X \times \Real^\infty$. |