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K-connectedness and the homotopy-lifting property

  1. May 26, 2010 #1
    Is there a relation between k-connectedness ( meaning 1st, 2nd,..,k-th fundamental
    groups are trivial.) and having the homotopy-lifting property.? . This may be
    vaguely-related to being able to extend global sections from the j-th skeleton, to
    the (j+1)-st skeleton (j<=k, obviously), but I am not sure.

    How about k-connectedness for a pair (A,X) ( A a subspace of X).

  2. jcsd
  3. May 27, 2010 #2
    Could you be more specific? Are we fixing a triple, or are we asking about whether any surjective map is a fibration?
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