blob to-do
author Kevin Walker <kevin@canyon23.net>
Wed, 11 May 2011 14:20:10 -0700
changeset 777 682fd0520c66
parent 776 c24e59300fca
child 778 760cc71a0424
permissions -rw-r--r--
added a sentence about conditions of existence of path integrals (at PT's request); other minor stuff


* 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

* (?) 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?]
	- add one more sentence: ~"finite dimensional and pos. def"

* 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:

* Marked hemispheres, need better language.
	- add something like "The is just a ball (\bd N \ N) with its entire boundary (\nd N) marked.  We use the term hemisphere because these balls are half the boundary of a larger ball.

* 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