# HG changeset patch # User Kevin Walker # Date 1319407450 21600 # Node ID 259bef1b5dad8b4dc125f8cd57f0e9e9b2d486b8 # Parent 80fe92f8f81f7c0c4c190575edd10aeba6fd3236 make claims about framed balls and non-pivotal n-cats weaker diff -r 80fe92f8f81f -r 259bef1b5dad blob to-do --- a/blob to-do Sun Oct 23 15:03:53 2011 -0600 +++ b/blob to-do Sun Oct 23 16:04:10 2011 -0600 @@ -1,15 +1,12 @@ ====== big ====== -* framings and duality -- work out what's going on! (alternatively, vague-ify current statement) - - ====== minor/optional ====== -* consider proving the gluing formula for higher codimension manifolds with +[probably NO] * 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. +[probably NO] * 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) @@ -17,10 +14,14 @@ * review colors in figures * better discussion of systems of fields from disk-like n-cats - (Is this done by now?) +*** Is this done by now? -* make sure we are clear that boundary = germ (perhaps we are already clear enough) +* make sure we are clear that boundary = germ +*** perhaps we are already clear enough +* framings and duality -- work out what's going on! (alternatively, vague-ify current statement) +*** is the new version sufficiently vague? + ====== Scott ====== diff -r 80fe92f8f81f -r 259bef1b5dad text/ncat.tex --- a/text/ncat.tex Sun Oct 23 15:03:53 2011 -0600 +++ b/text/ncat.tex Sun Oct 23 16:04:10 2011 -0600 @@ -100,10 +100,10 @@ The first is balls equipped with a map to some other space $Y$ (c.f. \cite{MR2079378}). This will be used below (see the end of \S \ref{ss:product-formula}) to describe the blob complex of a fiber bundle with base space $Y$. -The second is balls equipped with a section of the tangent bundle, or the frame +The second is balls equipped (partially defined) sections of the tangent bundle, or the frame bundle (i.e.\ framed balls), or more generally some partial flag bundle associated to the tangent bundle. These can be used to define categories with less than the ``strong" duality we assume here, -though we will not develop that idea fully in this paper. +though we will not develop that idea in this paper. Next we consider domains and ranges of morphisms (or, as we prefer to say, boundaries of morphisms).