1 

     2 * We need to be clearer about which types of homeomorphisms the

     3 "localization" theorem in the appendix works for, in the body of the

     4 paper. Options here include:

     5 a) having a better theorem in a separate paper, so we don't actually

     6 need to worry 

     7 [** currently working on this option]

     8 b) changing the statements in the paper, for example writing PL-Homeo

     9 everywhere instead of Homeo

    10 c) explicitly saying "Homeo means PL-Homeo" everywhere

    11 c') if we succumb to Peter's suggestion of say "Iso" everywhere,

    12 perhaps we could adopt the notation that "Iso^*" or similar means one

    13 of a restricted set of categories, where the appendix works, and using

    14 this notation in section 5.

    15 

    16 * Consider moving A_\infty stuff to a subsection

    17 

    18 * dimension n+1, explain the statement and refer to KW's notes

    19 

    20 * framings and duality -- work out what's going on!

    21 

    22 * consider proving the gluing formula for higher codimension manifolds with

    23 morita equivalence

    24 

    25 

    26 * Peter's suggestion for A_inf definition

    27 

    28 * enriching in other \infty categories, explaining how "D" should

    29 interact with coproducts in "S" (break out A_\infty stuff into a

    30 subsection)

    31 

    32 

    33 * SCOTT will go through appendix C.2 and make it better

    34 

    35 * In the appendix on n=1, explain more about orientations. Also say

    36 what happens on objects for spin manifolds: the unique point has an

    37 automorphism, which translates into a involution on objects. Mention

    38 super-stuff.

    39 

    40 * make remarks about defect interpretation of sphere modules

    41 

    42 

    43 colimit subsection: 

    44 

    45 * Labeling of the k-1 skeleton agreeing on the k-2 skeleton is awfully vague. 

    46 

    47 * Category of permissible decompositions must be a small category in order to take the colimit. 

    48 

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

    50 

    51 

    52 modules:

    53 

    54 * Marked hemispheres, need better language.

    55 

    56 * Lemma 6.4.5 needs to actually construct this map! Needs more input! Do

    57 we actually need this as written?

    58 

    59 

    60 

    61 * add remark about relation of SC operad to Ryan Budney thing

    62 

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

    64 

    65 * finalize acknowledge list

    66 

    67 * fix "cell decomposition" (\nn remark) in string-diagram-fields def

    68