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247 One replaces intervals with manifolds diffeomorphic to the ball $B^n$. |
247 One replaces intervals with manifolds diffeomorphic to the ball $B^n$. |
248 Marked points are replaced by copies of $B^{n-1}$ in $\bdy B^n$. |
248 Marked points are replaced by copies of $B^{n-1}$ in $\bdy B^n$. |
249 |
249 |
250 \nn{give examples: $A(J^n) = \bc_*(Z\times J)$ and $A(J^n) = C_*(\Maps(J \to M))$.} |
250 \nn{give examples: $A(J^n) = \bc_*(Z\times J)$ and $A(J^n) = C_*(\Maps(J \to M))$.} |
251 |
251 |
252 \todo{the motivating example $C_*(\maps(X, M))$} |
252 \todo{the motivating example $C_*(\Maps(X, M))$} |
253 |
253 |
254 |
254 |
255 |
255 |
256 \newcommand{\skel}[1]{\operatorname{skeleton}(#1)} |
256 \newcommand{\skel}[1]{\operatorname{skeleton}(#1)} |
257 |
257 |
404 \begin{itemize} |
404 \begin{itemize} |
405 \item recall defs of $A_\infty$ category (1-category only), modules, (self-) tensor product. |
405 \item recall defs of $A_\infty$ category (1-category only), modules, (self-) tensor product. |
406 use graphical/tree point of view, rather than following Keller exactly |
406 use graphical/tree point of view, rather than following Keller exactly |
407 \item define blob complex in $A_\infty$ case; fat mapping cones? tree decoration? |
407 \item define blob complex in $A_\infty$ case; fat mapping cones? tree decoration? |
408 \item topological $A_\infty$ cat def (maybe this should go first); also modules gluing |
408 \item topological $A_\infty$ cat def (maybe this should go first); also modules gluing |
409 \item motivating example: $C_*(\maps(X, M))$ |
409 \item motivating example: $C_*(\Maps(X, M))$ |
410 \item maybe incorporate dual point of view (for $n=1$), where points get |
410 \item maybe incorporate dual point of view (for $n=1$), where points get |
411 object labels and intervals get 1-morphism labels |
411 object labels and intervals get 1-morphism labels |
412 \end{itemize} |
412 \end{itemize} |
413 |
413 |
414 |
414 |