author | Kevin Walker <kevin@canyon23.net> |
Fri, 13 May 2011 20:52:18 -0700 | |
changeset 781 | 0a9adf027f47 |
parent 780 | b76b4b79dbe1 |
child 782 | d8ae97449506 |
permissions | -rw-r--r-- |
768 | 1 |
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* We need to be clearer about which types of homeomorphisms the |
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"localization" theorem in the appendix works for, in the body of the |
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paper. Options here include: |
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a) having a better theorem in a separate paper, so we don't actually |
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need to worry |
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[** currently working on this option] |
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b) changing the statements in the paper, for example writing PL-Homeo |
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everywhere instead of Homeo |
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c) explicitly saying "Homeo means PL-Homeo" everywhere |
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c') if we succumb to Peter's suggestion of say "Iso" everywhere, |
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perhaps we could adopt the notation that "Iso^*" or similar means one |
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of a restricted set of categories, where the appendix works, and using |
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this notation in section 5. |
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* Consider moving A_\infty stuff to a subsection |
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* (?) dimension n+1, explain the statement and refer to KW's notes. [this was PT's suggestion, but it's sort of already in there. do we need to do more?] |
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- add one more sentence: ~"finite dimensional and pos. def" |
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* framings and duality -- work out what's going on! (alternatively, vague-ify current statement) |
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* consider proving the gluing formula for higher codimension manifolds with |
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morita equivalence |
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* Peter's suggestion for A_inf definition |
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* enriching in other \infty categories, explaining how "D" should |
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interact with coproducts in "S" (break out A_\infty stuff into a |
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subsection) |
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* SCOTT will go through appendix C.2 and make it better |
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* In the appendix on n=1, explain more about orientations. Also say |
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what happens on objects for spin manifolds: the unique point has an |
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automorphism, which translates into a involution on objects. Mention |
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super-stuff. |
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colimit subsection: |
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* Labeling of the k-1 skeleton agreeing on the k-2 skeleton is awfully vague. |
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* Boundary of \cl; not so easy to see! |
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modules: |
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* Lemma 6.4.5 needs to actually construct this map! Needs more input! Do |
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we actually need this as written? |
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- KW will look at it; probably needs to be weakened |
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* SCOTT: typo in delfig3a -- upper g should be g^{-1} |
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769
c861ec0b1554
minor: remove \nn from ack list; shorten lines; remove some comments
Kevin Walker <kevin@canyon23.net>
parents:
768
diff
changeset
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* SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar (I think I have all the speakers) |
768 | 60 |
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773
775b5ca42bed
make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents:
772
diff
changeset
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775b5ca42bed
make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents:
772
diff
changeset
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* review colors in figures |
775b5ca42bed
make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents:
772
diff
changeset
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775b5ca42bed
make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents:
772
diff
changeset
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* ? define Morita equivalence? |
775b5ca42bed
make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents:
772
diff
changeset
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774 | 66 |
* make sure we are clear that boundary = germ |
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* lemma [inject 6.3.5?] assumes more splittablity than the axioms imply (?) |
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0a9adf027f47
rewriting colimit def; there's still a little more to do
Kevin Walker <kevin@canyon23.net>
parents:
780
diff
changeset
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* SCOTT: figure for example 3.1.2 (sin 1/z) |
780
b76b4b79dbe1
starting to work on colimit stuff, but not much progress yet
Kevin Walker <kevin@canyon23.net>
parents:
776
diff
changeset
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781
0a9adf027f47
rewriting colimit def; there's still a little more to do
Kevin Walker <kevin@canyon23.net>
parents:
780
diff
changeset
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72 |
* SCOTT: add vertical arrow to middle of figure 19 (decomp poset) |
0a9adf027f47
rewriting colimit def; there's still a little more to do
Kevin Walker <kevin@canyon23.net>
parents:
780
diff
changeset
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73 |