blob to-do
author Kevin Walker <kevin@canyon23.net>
Wed, 12 Oct 2011 15:10:54 -0700
changeset 905 7afa2ffbbac8
parent 900 2efd26072c91
child 909 f194ed15587b
permissions -rw-r--r--
operad action only up to homotopy; still need to think about this a bit


====== big ======

* better discussion of systems of fields from disk-like n-cats
    (Is this done by now?)
    
* double-check for mentions of TOP

* (maybe) say somewhere what's missing for TOP

* 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

* probably should go through and refer to new splitting axiom when we need to choose refinements etc.
**** in the proof that gluing in dimension < n is injective

* revisit splitting axiom for system of fields; check use of it in small blobs lemma

* framings and duality -- work out what's going on! (alternatively, vague-ify current statement)

* make sure we are clear that boundary = germ (perhaps we are already clear enough)


* places splitting axiom is used:
** in the proof that gluing in dimension < n is injective
** in the proof that D(a) is acyclic
** in the small blobs lemma



====== minor/optional ======

* consider proving the gluing formula for higher codimension manifolds with
morita equivalence

* 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.

* 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
(but since the strict version of this is true for BT_*, maybe we're OK)

* review colors in figures


====== Scott ======

* SCOTT will go through appendix C.2 and make it better (Schulman's example?)

* SCOTT: review/proof-read recent KW changes, especially colimit section and n-cat axioms