Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorAndrew Stacey
   • CommentTimeDec 16th 2011
   • PermaLink
   Author: Andrew Stacey
   Format: MarkdownItexThis was posted on the "container" *Mathforge* forum. I left a message saying that it should be reposted here and that I would delete it after a few days. It hasn't been reposted here, but I'm going to delete it now so I'm recording it here for posterity. Although we can use this as a guide to making some things clearer on the nLab (which I believe that Urs has already done), there's no point in trying to respond *here* until the questioner turns up. > a naive question ? > This is about the notion of "smooth path", which is fundamental for holonomy. > Does that mean that it admits a smooth parametrizing ? I mean infintely derivable ? If so, I do not understantd how it could admit "sitting instants" because I naively believe that it a smooth function has all derivatives zero, or is zero on an open set, it should be zero everywhere. > I am sure I am wrong somewhere, but where ? > many thanks > (a second question It is clear for me that holonomy compose by group product for smooth spaces. But it seems that it does not for non smooth ones : if there is a discontinuity of the derivative at the joining point, one has to add a corresponding element of the group (corresponding to the rotation at that point). Am I right ?)

   This was posted on the “container” Mathforge forum. I left a message saying that it should be reposted here and that I would delete it after a few days. It hasn’t been reposted here, but I’m going to delete it now so I’m recording it here for posterity. Although we can use this as a guide to making some things clearer on the nLab (which I believe that Urs has already done), there’s no point in trying to respond here until the questioner turns up.

   a naive question ?

   This is about the notion of “smooth path”, which is fundamental for holonomy.

   Does that mean that it admits a smooth parametrizing ? I mean infintely derivable ? If so, I do not understantd how it could admit “sitting instants” because I naively believe that it a smooth function has all derivatives zero, or is zero on an open set, it should be zero everywhere.

   I am sure I am wrong somewhere, but where ?

   many thanks

   (a second question It is clear for me that holonomy compose by group product for smooth spaces. But it seems that it does not for non smooth ones : if there is a discontinuity of the derivative at the joining point, one has to add a corresponding element of the group (corresponding to the rotation at that point). Am I right ?)

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 16th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexJust for the record: we have dealt with that [here](http://www.math.ntnu.no/~stacey/Mathforge/nForum/comments.php?DiscussionID=3360&page=1#Item_1).

   Just for the record: we have dealt with that here.