# HG changeset patch # User Kevin Walker # Date 1275337644 25200 # Node ID 62d112a2df120a0702c8d24a917ab766008e7d02 # Parent ee7be19ee61a67dabea507a37f7f22bdcf57f11f mention some other flavors of balls diff -r ee7be19ee61a -r 62d112a2df12 text/ncat.tex --- a/text/ncat.tex Mon May 31 12:44:19 2010 -0700 +++ b/text/ncat.tex Mon May 31 13:27:24 2010 -0700 @@ -73,6 +73,15 @@ For each flavor of manifold there is a corresponding flavor of $n$-category. We will concentrate on the case of PL unoriented manifolds. +(The ambitious reader may want to keep in mind two other classes of balls. +The first is balls equipped with a map to some other space $Y$. +This will be used below to describe the blob complex of a fiber bundle with +base space $Y$. +The second is balls equipped with a section of the the tangent bundle, or the frame +bundle (i.e.\ framed balls), or more generally some 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.) + Next we consider domains and ranges of morphisms (or, as we prefer to say, boundaries of morphisms). The 0-sphere is unusual among spheres in that it is disconnected.