blob to-do
author Kevin Walker <kevin@canyon23.net>
Fri, 06 May 2011 18:02:06 -0700
changeset 768 d8151afc725e
child 769 c861ec0b1554
permissions -rw-r--r--
adding to-do list
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
768
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     1
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     2
* We need to be clearer about which types of homeomorphisms the
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     3
"localization" theorem in the appendix works for, in the body of the
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     4
paper. Options here include:
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     5
a) having a better theorem in a separate paper, so we don't actually
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     6
need to worry 
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     7
[** currently working on this option]
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     8
b) changing the statements in the paper, for example writing PL-Homeo
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
     9
everywhere instead of Homeo
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    10
c) explicitly saying "Homeo means PL-Homeo" everywhere
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    11
c') if we succumb to Peter's suggestion of say "Iso" everywhere,
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    12
perhaps we could adopt the notation that "Iso^*" or similar means one
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    13
of a restricted set of categories, where the appendix works, and using
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    14
this notation in section 5.
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    15
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    16
* Consider moving A_\infty stuff to a subsection
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    17
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    18
* dimension n+1, explain the statement and refer to KW's notes
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    19
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    20
* framings and duality -- work out what's going on!
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    21
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    22
* consider proving the gluing formula for higher codimension manifolds with
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    23
morita equivalence
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    24
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    25
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    26
* Peter's suggestion for A_inf definition
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    27
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    28
* enriching in other \infty categories, explaining how "D" should
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    29
interact with coproducts in "S" (break out A_\infty stuff into a
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    30
subsection)
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    31
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    32
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    33
* SCOTT will go through appendix C.2 and make it better
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    34
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    35
* In the appendix on n=1, explain more about orientations. Also say
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    36
what happens on objects for spin manifolds: the unique point has an
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    37
automorphism, which translates into a involution on objects. Mention
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    38
super-stuff.
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    39
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    40
* make remarks about defect interpretation of sphere modules
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    41
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    42
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    43
colimit subsection: 
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    44
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    45
* Labeling of the k-1 skeleton agreeing on the k-2 skeleton is awfully vague. 
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    46
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    47
* Category of permissible decompositions must be a small category in order to take the colimit. 
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    48
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    49
* Boundary of \cl; not so easy to see!
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    50
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    51
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    52
modules:
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    53
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    54
* Marked hemispheres, need better language.
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    55
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    56
* Lemma 6.4.5 needs to actually construct this map! Needs more input! Do
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    57
we actually need this as written?
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    58
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    59
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    60
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    61
* add remark about relation of SC operad to Ryan Budney thing
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    62
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    63
* SCOTT: typo in delfig3a -- upper g should be g^{-1}
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    64
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    65
* finalize acknowledge list
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    66
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    67
* fix "cell decomposition" (\nn remark) in string-diagram-fields def
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    68