blob to-do
author Kevin Walker <kevin@canyon23.net>
Thu, 12 May 2011 21:42:34 -0700
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child 781 0a9adf027f47
permissions -rw-r--r--
starting to work on colimit stuff, but not much progress yet
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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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* SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar (I think I have all the speakers)
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* review colors in figures
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* ? define Morita equivalence?
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* 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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* figure for example 3.1.2 (sin 1/z)
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