diff -r 787914e9e859 -r ec8587c33c0b blob to-do --- a/blob to-do Sat May 28 09:49:30 2011 -0600 +++ b/blob to-do Sat May 28 21:45:13 2011 -0600 @@ -1,71 +1,51 @@ -* 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. +* extend localization lemma to (topological) homeos + +* lemma [inject 6.3.5?] assumes more splittablity than the axioms imply (?) + * Consider moving A_\infty stuff to a subsection +* consider putting conditions for enriched n-cat all in one place + +* Peter's suggestion for A_inf definition + +* Boundary of colimit -- not so easy to see! + +* ** new material in colimit section needs a proof-read + +* 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. [partly done] + + +* should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable + * framings and duality -- work out what's going on! (alternatively, vague-ify current statement) +* make sure we are clear that boundary = germ + +* review colors in figures + +* maybe say something in colimit section about restriction to submanifolds and submanifolds of boundary (we use this in n-cat axioms) + + +* ? define Morita equivalence? + * 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 \ No newline at end of file