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1 |
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2 * We need to be clearer about which types of homeomorphisms the |
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3 "localization" theorem in the appendix works for, in the body of the |
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4 paper. Options here include: |
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5 a) having a better theorem in a separate paper, so we don't actually |
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6 need to worry |
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7 [** currently working on this option] |
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8 b) changing the statements in the paper, for example writing PL-Homeo |
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9 everywhere instead of Homeo |
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10 c) explicitly saying "Homeo means PL-Homeo" everywhere |
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11 c') if we succumb to Peter's suggestion of say "Iso" everywhere, |
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12 perhaps we could adopt the notation that "Iso^*" or similar means one |
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13 of a restricted set of categories, where the appendix works, and using |
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14 this notation in section 5. |
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15 |
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16 * Consider moving A_\infty stuff to a subsection |
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17 |
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18 * dimension n+1, explain the statement and refer to KW's notes |
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19 |
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20 * framings and duality -- work out what's going on! |
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21 |
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22 * consider proving the gluing formula for higher codimension manifolds with |
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23 morita equivalence |
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24 |
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25 |
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26 * Peter's suggestion for A_inf definition |
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27 |
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28 * enriching in other \infty categories, explaining how "D" should |
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29 interact with coproducts in "S" (break out A_\infty stuff into a |
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30 subsection) |
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31 |
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32 |
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33 * SCOTT will go through appendix C.2 and make it better |
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34 |
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35 * In the appendix on n=1, explain more about orientations. Also say |
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36 what happens on objects for spin manifolds: the unique point has an |
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37 automorphism, which translates into a involution on objects. Mention |
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38 super-stuff. |
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39 |
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40 * make remarks about defect interpretation of sphere modules |
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41 |
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42 |
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43 colimit subsection: |
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44 |
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45 * Labeling of the k-1 skeleton agreeing on the k-2 skeleton is awfully vague. |
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46 |
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47 * Category of permissible decompositions must be a small category in order to take the colimit. |
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48 |
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49 * Boundary of \cl; not so easy to see! |
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50 |
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51 |
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52 modules: |
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53 |
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54 * Marked hemispheres, need better language. |
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55 |
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56 * Lemma 6.4.5 needs to actually construct this map! Needs more input! Do |
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57 we actually need this as written? |
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58 |
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59 |
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60 |
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61 * add remark about relation of SC operad to Ryan Budney thing |
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62 |
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63 * SCOTT: typo in delfig3a -- upper g should be g^{-1} |
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64 |
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65 * finalize acknowledge list |
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66 |
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67 * fix "cell decomposition" (\nn remark) in string-diagram-fields def |
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68 |