Not signed in (Sign In)

Start a new discussion

Not signed in

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

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2017

    The term “flow of a vector field” used to redirect to exponential map, which however is really concerned with a somewhat different concept. So I have created now a separate entry flow of a vector field.

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 26th 2017
    • (edited Jun 26th 2017)

    We have some SDG constructions elsewhere. Worth including here? Something like

    A tangent vector field is a section of the map of X DXX^D \to X corresponding to evaluation at 0, so is a map f:XX Df: X \to X^D, such that f(x)(0)=xf(x)(0) = x. Uncurrying, this is equivalent to a map f *:X×DXf^{\ast}:X \times D \to X, with f *(x,0)=xf^{\ast} (x, 0) = x. Currying the first variable yields a map DX XD \to X^X, i.e., to the group of diffeomorphisms of XX.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2017

    Okay, I wrote something here. Unfortunately I don’t really have the leisure for this at the moment

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 26th 2017

    Great, thanks. I linked to it from synthetic differential geometry.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)