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
    • CommentTimeApr 1st 2016

    at Serre fibration I have spelled out the proof that that with F xXfibYF_x \hookrightarrow X \overset{fib}{\to} Y then π (F)π (X)π (Y)\pi_\bullet(F) \to \pi_\bullet(X)\to \pi_{\bullet(Y)} is exact in the middle. here.

    (This is intentionally the low-technology proof using nothing but the definition. )

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 18th 2017

    Added to Serre fibration a section Properties – Relation to Hurewicz fibrations with pointer to

    a) counter-example of a Serre fibration that is not a Hurewicz fibration

    b) statement that all Serre fibrations between CW-complexes are Hurewicz fibrations.

    Also added to the Examples-section pointer to the homotopy lifting property for covering spaces.

    • CommentRowNumber3.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 19th 2017

    (The projection map of) a fibre bundle over any paracompact space, or more generally, a bundle that admits a trivialisation over a numerable cover, is a Hurewicz fibration, I believe.. In general, all fibre bundles are Serre fibrations.

    (I was torn between adding this comment here or at the covering space thread)

    • CommentRowNumber4.
    • CommentAuthorDexter Chua
    • CommentTimeJul 29th 2017

    Fixed some syntax errors

    • CommentRowNumber5.
    • CommentAuthorTim_Porter
    • CommentTimeDec 29th 2018

    The ’in particulars’ were ’breeding thick and fast’ in certain parts of this page! I removed one of them to keep the population down.

    diff, v17, current

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)