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2 * We need to be clearer about which types of homeomorphisms the |
2 * extend localization lemma to (topological) homeos |
3 "localization" theorem in the appendix works for, in the body of the |
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4 paper. Options here include: |
4 * lemma [inject 6.3.5?] assumes more splittablity than the axioms imply (?) |
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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16 * Consider moving A_\infty stuff to a subsection |
7 * Consider moving A_\infty stuff to a subsection |
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9 * consider putting conditions for enriched n-cat all in one place |
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11 * Peter's suggestion for A_inf definition |
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13 * Boundary of colimit -- not so easy to see! |
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15 * ** new material in colimit section needs a proof-read |
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17 * In the appendix on n=1, explain more about orientations. Also say |
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18 what happens on objects for spin manifolds: the unique point has an |
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19 automorphism, which translates into a involution on objects. Mention |
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20 super-stuff. [partly done] |
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23 * should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable |
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18 * framings and duality -- work out what's going on! (alternatively, vague-ify current statement) |
25 * framings and duality -- work out what's going on! (alternatively, vague-ify current statement) |
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26 |
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27 * make sure we are clear that boundary = germ |
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28 |
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29 * review colors in figures |
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31 * maybe say something in colimit section about restriction to submanifolds and submanifolds of boundary (we use this in n-cat axioms) |
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33 |
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34 * ? define Morita equivalence? |
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20 * consider proving the gluing formula for higher codimension manifolds with |
36 * consider proving the gluing formula for higher codimension manifolds with |
21 morita equivalence |
37 morita equivalence |
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24 * Peter's suggestion for A_inf definition |
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26 * enriching in other \infty categories, explaining how "D" should |
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27 interact with coproducts in "S" (break out A_\infty stuff into a |
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28 subsection) |
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31 * SCOTT will go through appendix C.2 and make it better |
41 * SCOTT will go through appendix C.2 and make it better |
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33 * make sure we are clear that boundary = germ |
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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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40 |
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41 colimit subsection: |
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42 |
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43 * Boundary of \cl; not so easy to see! |
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44 |
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45 * new material in colimit section needs a proof-read |
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47 |
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48 modules: |
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50 * SCOTT: typo in delfig3a -- upper g should be g^{-1} |
43 * SCOTT: typo in delfig3a -- upper g should be g^{-1} |
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52 * SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar who should be included (I think I have all the speakers; does anyone other than the speakers rate a mention?) |
45 * SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar who should be included (I think I have all the speakers; does anyone other than the speakers rate a mention?) |
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54 |
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55 * review colors in figures |
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56 |
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57 * ? define Morita equivalence? |
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58 |
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59 * lemma [inject 6.3.5?] assumes more splittablity than the axioms imply (?) |
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60 |
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61 * consider putting conditions for enriched n-cat all in one place |
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62 |
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63 * SCOTT: figure for example 3.1.2 (sin 1/z) |
47 * SCOTT: figure for example 3.1.2 (sin 1/z) |
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65 * SCOTT: add vertical arrow to middle of figure 19 (decomp poset) |
49 * SCOTT: add vertical arrow to middle of figure 19 (decomp poset) |
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67 * maybe say something in colimit section about restriction to submanifolds and submanifolds of boundary |
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68 |
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69 * SCOTT: review/proof-read recent KW changes |
51 * SCOTT: review/proof-read recent KW changes |
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71 * should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable |
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