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479 |
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481 \medskip |
481 \medskip |
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484 \hrule\medskip\hrule\medskip |
485 |
485 |
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486 \nn{outline of what remains to be done:} |
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487 |
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488 \begin{itemize} |
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489 \item We need to assemble the maps for the various $G^{i,m}$ into |
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490 a map for all of $CD_*\ot \bc_*$. |
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491 One idea: Think of the $g_j$ as a sort of homotopy (from $CD_*\ot \bc_*$ to itself) |
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492 parameterized by $[0,\infty)$. For each $p\ot b$ in $CD_*\ot \bc_*$ choose a sufficiently |
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493 large $j'$. Use these choices to reparameterize $g_\bullet$ so that each |
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494 $p\ot b$ gets pushed as far as the corresponding $j'$. |
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495 \item Independence of metric, $\ep_i$, $\delta_i$: |
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496 For a different metric etc. let $\hat{G}^{i,m}$ denote the alternate subcomplexes |
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497 and $\hat{N}_{i,l}$ the alternate neighborhoods. |
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498 Main idea is that for all $i$ there exists sufficiently large $k$ such that |
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499 $\hat{N}_{k,l} \sub N_{i,l}$, and similarly with the roles of $N$ and $\hat{N}$ reversed. |
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500 \item Also need to prove associativity. |
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501 \end{itemize} |
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502 |
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503 |
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504 \nn{to be continued....} |
486 |
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487 \noop{ |
506 \noop{ |
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489 \begin{lemma} |
508 \begin{lemma} |
490 |
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495 \end{proof} |
514 \end{proof} |
496 |
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497 } |
516 } |
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500 \nn{to be continued....} |
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501 |
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503 %\nn{say something about associativity here} |
521 %\nn{say something about associativity here} |
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