author | Scott Morrison <scott@tqft.net> |
Tue, 09 Aug 2011 23:22:07 -0700 | |
changeset 864 | 296fcf7e5914 |
parent 850 | 38955cc8e1a7 |
child 878 | 937214896458 |
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
changeset
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839 | 4 |
* better discussion of systems of fields from disk-like n-cats |
850 | 5 |
(Is this done by now?) |
823 | 6 |
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821
6868130229bf
minor; out of time for now
Kevin Walker <kevin@canyon23.net>
parents:
818
diff
changeset
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7 |
* need to fix fam-o-homeo argument per discussion with Rob |
6868130229bf
minor; out of time for now
Kevin Walker <kevin@canyon23.net>
parents:
818
diff
changeset
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8 |
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801
33b3e0c065d2
adding placeholder figure
Kevin Walker <kevin@canyon23.net>
parents:
800
diff
changeset
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9 |
* 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 | 10 |
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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
|
11 |
* probably should go through and refer to new splitting axiom when we need to choose refinements etc. |
836 | 12 |
** in the proof that gluing in dimension < n is injective |
790
ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
787
diff
changeset
|
13 |
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776 | 14 |
* framings and duality -- work out what's going on! (alternatively, vague-ify current statement) |
768 | 15 |
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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
|
16 |
* 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
|
17 |
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ec8587c33c0b
more details in C.1; reorganized to-do list
Kevin Walker <kevin@canyon23.net>
parents:
787
diff
changeset
|
18 |
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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
|
19 |
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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
|
20 |
====== 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
|
21 |
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768 | 22 |
* consider proving the gluing formula for higher codimension manifolds with |
23 |
morita equivalence |
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24 |
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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
|
25 |
* 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
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26 |
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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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27 |
* 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
|
28 |
(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
|
29 |
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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
|
30 |
* 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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31 |
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768 | 32 |
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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
|
33 |
====== Scott ====== |
768 | 34 |
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35 |
* SCOTT will go through appendix C.2 and make it better |
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36 |
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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
|
37 |
* SCOTT: review/proof-read recent KW changes, especially colimit section and n-cat axioms |