Results 1 to 3 of 3

Math Help - Homotopy Group Question

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    37

    Homotopy Group Question

    I'm working out a proof for topology:

    If a topological space has a trivial fundamental group, can you establish that all higher homotopy groups of that same space are also trivial?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member
    Joined
    May 2008
    Posts
    37
    I found a resource online that said that all higher homotopy groups are trivial if the space is contractible, but can you say anything stronger? And how would you show this?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by joeyjoejoe View Post
    I'm working out a proof for topology:

    If a topological space has a trivial fundamental group, can you establish that all higher homotopy groups of that same space are also trivial?
    Hint: think about spheres ( S^2 in particular).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Composition of homotopy equivalences is a homotopy equivalence.
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 30th 2011, 08:33 PM
  2. Topology (specifically homotopy) question!
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: January 28th 2011, 05:28 AM
  3. homotopy
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: July 23rd 2010, 05:09 AM
  4. homotopy
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: June 10th 2010, 05:20 AM
  5. Group Theory Question, Dihedral Group
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: March 4th 2008, 10:36 AM

Search Tags


/mathhelpforum @mathhelpforum