blob to-do
author Kevin Walker <kevin@canyon23.net>
Sun, 19 Jun 2011 15:31:28 -0600
changeset 800 d0b9238aad5d
parent 798 bc8de6442481
child 801 33b3e0c065d2
permissions -rw-r--r--
new n-cat axiom for splittings
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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* lemma [inject  6.3.5?] assumes more splittablity than the axioms imply (?)
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* need to change module axioms to follow changes in n-cat axioms; search for and destroy all the "Homeo_\bd"'s
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* Boundary of colimit -- not so easy to see!
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* ** new material in colimit section needs a proof-read
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* should probably allow product things \pi^*(b) to be defined only when b is appropriately splittable
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* framings and duality -- work out what's going on! (alternatively, vague-ify current statement)
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* make sure we are clear that boundary = germ
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* go through text and remove any disclaimers about continuous (as oppsed to PL) homeos
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* review colors in figures
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* maybe say something in colimit section about restriction to submanifolds and submanifolds of boundary (we use this in n-cat axioms)
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* ? define Morita equivalence?
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* consider proving the gluing formula for higher codimension manifolds with
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morita equivalence
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* 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.
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* 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
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(but since the strict version of this is true for BT_*, maybe we're OK)
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* probably should go through and refer to new splitting axiom when we need to choose refinements etc.
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* SCOTT will go through appendix C.2 and make it better
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* SCOTT: typo in delfig3a -- upper g should be g^{-1}
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* 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?)
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* SCOTT: figure for example 3.1.2 (sin 1/z)
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* SCOTT: add vertical arrow to middle of figure 19 (decomp poset)
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* SCOTT: review/proof-read recent KW changes