* We need to be clearer about which types of homeomorphisms the
"localization" theorem in the appendix works for, in the body of the
paper. Options here include:
a) having a better theorem in a separate paper, so we don't actually
need to worry
[** currently working on this option]
b) changing the statements in the paper, for example writing PL-Homeo
everywhere instead of Homeo
c) explicitly saying "Homeo means PL-Homeo" everywhere
c') if we succumb to Peter's suggestion of say "Iso" everywhere,
perhaps we could adopt the notation that "Iso^*" or similar means one
of a restricted set of categories, where the appendix works, and using
this notation in section 5.
* Consider moving A_\infty stuff to a subsection
* framings and duality -- work out what's going on! (alternatively, vague-ify current statement)
* consider proving the gluing formula for higher codimension manifolds with
morita equivalence
* Peter's suggestion for A_inf definition
* enriching in other \infty categories, explaining how "D" should
interact with coproducts in "S" (break out A_\infty stuff into a
subsection)
* SCOTT will go through appendix C.2 and make it better
* In the appendix on n=1, explain more about orientations. Also say
what happens on objects for spin manifolds: the unique point has an
automorphism, which translates into a involution on objects. Mention
super-stuff.
colimit subsection:
* Labeling of the k-1 skeleton agreeing on the k-2 skeleton is awfully vague.
* Boundary of \cl; not so easy to see!
modules:
* Lemma 6.4.5 needs to actually construct this map! Needs more input! Do
we actually need this as written?
- KW will look at it; probably needs to be weakened
* SCOTT: typo in delfig3a -- upper g should be g^{-1}
* SCOTT: make sure acknowledge list doesn't omit anyone from blob seminar (I think I have all the speakers)
* review colors in figures
* ? define Morita equivalence?
* make sure we are clear that boundary = germ
* lemma [inject 6.3.5?] assumes more splittablity than the axioms imply (?)
* consider putting conditions for enriched n-cat all in one place