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
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
776
c24e59300fca updated to-do list
Kevin Walker <kevin@canyon23.net>
parents: 774
diff changeset
    18
* framings and duality -- work out what's going on! (alternatively, vague-ify current statement)
768
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
* consider proving the gluing formula for higher codimension manifolds with
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    21
morita equivalence
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    22
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    23
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    24
* Peter's suggestion for A_inf definition
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
* enriching in other \infty categories, explaining how "D" should
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    27
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
    28
subsection)
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    29
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    30
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    31
* SCOTT will go through appendix C.2 and make it better
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    32
784
bd9538de8248 more on colimits; still not done
Kevin Walker <kevin@canyon23.net>
parents: 783
diff changeset
    33
* make sure we are clear that boundary = germ
bd9538de8248 more on colimits; still not done
Kevin Walker <kevin@canyon23.net>
parents: 783
diff changeset
    34
768
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
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    41
colimit subsection: 
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    42
783
Kevin Walker <kevin@canyon23.net>
parents: 782
diff changeset
    43
* Boundary of \cl; not so easy to see!
768
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    44
783
Kevin Walker <kevin@canyon23.net>
parents: 782
diff changeset
    45
* new material in colimit section needs a proof-read
768
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
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    48
modules:
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    49
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    50
* SCOTT: typo in delfig3a -- upper g should be g^{-1}
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    51
783
Kevin Walker <kevin@canyon23.net>
parents: 782
diff changeset
    52
* 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?)
768
d8151afc725e adding to-do list
Kevin Walker <kevin@canyon23.net>
parents:
diff changeset
    53
773
775b5ca42bed make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents: 772
diff changeset
    54
775b5ca42bed make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents: 772
diff changeset
    55
* review colors in figures
775b5ca42bed make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents: 772
diff changeset
    56
775b5ca42bed make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents: 772
diff changeset
    57
* ? define Morita equivalence?
775b5ca42bed make sure poset of decomps is a small category; added to to-do list
Kevin Walker <kevin@canyon23.net>
parents: 772
diff changeset
    58
776
c24e59300fca updated to-do list
Kevin Walker <kevin@canyon23.net>
parents: 774
diff changeset
    59
* lemma [inject  6.3.5?] assumes more splittablity than the axioms imply (?)
c24e59300fca updated to-do list
Kevin Walker <kevin@canyon23.net>
parents: 774
diff changeset
    60
777
682fd0520c66 added a sentence about conditions of existence of path integrals (at PT's request); other minor stuff
Kevin Walker <kevin@canyon23.net>
parents: 776
diff changeset
    61
* consider putting conditions for enriched n-cat all in one place
682fd0520c66 added a sentence about conditions of existence of path integrals (at PT's request); other minor stuff
Kevin Walker <kevin@canyon23.net>
parents: 776
diff changeset
    62
781
0a9adf027f47 rewriting colimit def; there's still a little more to do
Kevin Walker <kevin@canyon23.net>
parents: 780
diff changeset
    63
* SCOTT: figure for example 3.1.2 (sin 1/z)
780
b76b4b79dbe1 starting to work on colimit stuff, but not much progress yet
Kevin Walker <kevin@canyon23.net>
parents: 776
diff changeset
    64
781
0a9adf027f47 rewriting colimit def; there's still a little more to do
Kevin Walker <kevin@canyon23.net>
parents: 780
diff changeset
    65
* SCOTT: add vertical arrow to middle of figure 19 (decomp poset)
787
c0cdde54913a start to rearrange n-cat defs
Kevin Walker <kevin@canyon23.net>
parents: 786
diff changeset
    66
c0cdde54913a start to rearrange n-cat defs
Kevin Walker <kevin@canyon23.net>
parents: 786
diff changeset
    67
* maybe say something in colimit section about restriction to submanifolds and submanifolds of boundary
c0cdde54913a start to rearrange n-cat defs
Kevin Walker <kevin@canyon23.net>
parents: 786
diff changeset
    68
c0cdde54913a start to rearrange n-cat defs
Kevin Walker <kevin@canyon23.net>
parents: 786
diff changeset
    69
* SCOTT: review/proof-read recent KW changes
c0cdde54913a start to rearrange n-cat defs
Kevin Walker <kevin@canyon23.net>
parents: 786
diff changeset
    70
c0cdde54913a start to rearrange n-cat defs
Kevin Walker <kevin@canyon23.net>
parents: 786
diff changeset
    71
* should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable