author | Kevin Walker <kevin@canyon23.net> |
Tue, 04 Oct 2011 22:44:54 -0700 | |
changeset 898 | 14e05e9785c0 |
parent 896 | deeff619087e |
child 900 | 2efd26072c91 |
permissions | -rw-r--r-- |
803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
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1 |
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a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
2 |
====== big ====== |
790
ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
787
diff
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839 | 4 |
* better discussion of systems of fields from disk-like n-cats |
850 | 5 |
(Is this done by now?) |
878
937214896458
add referees request for comment on hh_*(loops)
Kevin Walker <kevin@canyon23.net>
parents:
850
diff
changeset
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6 |
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893 | 7 |
* double-check for mentions of TOP |
823 | 8 |
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893 | 9 |
* (maybe) say somewhere what's missing for TOP |
821
6868130229bf
minor; out of time for now
Kevin Walker <kevin@canyon23.net>
parents:
818
diff
changeset
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10 |
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801
33b3e0c065d2
adding placeholder figure
Kevin Walker <kevin@canyon23.net>
parents:
800
diff
changeset
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11 |
* need to change module axioms to follow changes in n-cat axioms; search for and destroy all the "Homeo_\bd"'s, add a v-cone axiom |
768 | 12 |
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803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
13 |
* probably should go through and refer to new splitting axiom when we need to choose refinements etc. |
896
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
14 |
**** in the proof that gluing in dimension < n is injective |
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
15 |
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deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
16 |
* revisit splitting axiom for system of fields; check use of it in small blobs lemma |
790
ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
787
diff
changeset
|
17 |
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776 | 18 |
* framings and duality -- work out what's going on! (alternatively, vague-ify current statement) |
768 | 19 |
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803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
20 |
* make sure we are clear that boundary = germ (perhaps we are already clear enough) |
790
ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
787
diff
changeset
|
21 |
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ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
787
diff
changeset
|
22 |
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896
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
23 |
* places splitting axiom is used: |
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
24 |
** in the proof that gluing in dimension < n is injective |
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
25 |
** in the proof that D(a) is acyclic |
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
26 |
** in the small blobs lemma |
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
27 |
|
deeff619087e
Initial version of the new splitting axiom.
Kevin Walker <kevin@canyon23.net>
parents:
893
diff
changeset
|
28 |
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803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
29 |
|
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
30 |
====== minor/optional ====== |
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
31 |
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768 | 32 |
* consider proving the gluing formula for higher codimension manifolds with |
33 |
morita equivalence |
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34 |
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796
d30537de52c7
in the midst of revising a-inf and enriched n-cat axioms; not done yet
Kevin Walker <kevin@canyon23.net>
parents:
794
diff
changeset
|
35 |
* leftover: we used to require that composition of A-infinity n-morphisms was injective (just like lower morphisms). Should we stick this back in? I don't think we use it anywhere. |
d30537de52c7
in the midst of revising a-inf and enriched n-cat axioms; not done yet
Kevin Walker <kevin@canyon23.net>
parents:
794
diff
changeset
|
36 |
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798
bc8de6442481
misc; added some specifics of acknowledgements
Kevin Walker <kevin@canyon23.net>
parents:
797
diff
changeset
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37 |
* should we require, for A-inf n-cats, that families which preserve product morphisms act trivially? as now defined, this is only true up to homotopy for the blob complex, so maybe best not to open that can of worms |
800
d0b9238aad5d
new n-cat axiom for splittings
Kevin Walker <kevin@canyon23.net>
parents:
798
diff
changeset
|
38 |
(but since the strict version of this is true for BT_*, maybe we're OK) |
d0b9238aad5d
new n-cat axiom for splittings
Kevin Walker <kevin@canyon23.net>
parents:
798
diff
changeset
|
39 |
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803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
40 |
* review colors in figures |
797
40729de8e067
finish fam-o-homeo axiom revisions and discussion
Kevin Walker <kevin@canyon23.net>
parents:
796
diff
changeset
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41 |
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768 | 42 |
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803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
43 |
====== Scott ====== |
768 | 44 |
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45 |
* SCOTT will go through appendix C.2 and make it better |
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46 |
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803
a96ffd48ea3d
wrote a little (but not enough) about Morita equivalence; out of time, will finish later
Kevin Walker <kevin@canyon23.net>
parents:
802
diff
changeset
|
47 |
* SCOTT: review/proof-read recent KW changes, especially colimit section and n-cat axioms |