blob to-do
author Kevin Walker <kevin@canyon23.net>
Fri, 27 May 2011 13:43:20 -0600
changeset 787 c0cdde54913a
parent 786 91d32d0cb2ef
child 790 ec8587c33c0b
permissions -rw-r--r--
start to rearrange n-cat defs


* 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

* make sure we are clear that boundary = germ

* 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: 

* Boundary of \cl; not so easy to see!

* new material in colimit section needs a proof-read


modules:

* SCOTT: typo in delfig3a -- upper g should be g^{-1}

* 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?)


* review colors in figures

* ? define Morita equivalence?

* lemma [inject  6.3.5?] assumes more splittablity than the axioms imply (?)

* consider putting conditions for enriched n-cat all in one place

* SCOTT: figure for example 3.1.2 (sin 1/z)

* SCOTT: add vertical arrow to middle of figure 19 (decomp poset)

* maybe say something in colimit section about restriction to submanifolds and submanifolds of boundary

* SCOTT: review/proof-read recent KW changes

* should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable