Results 1 to 3 of 3

Math Help - 2-fold covering spaces of the figure eight

  1. #1
    Member
    Joined
    Feb 2009
    Posts
    98

    2-fold covering spaces of the figure eight

    How do you construct all the 2-fold covering spaces (up to isomorphism) of the wedge of two circles?
    Do we use the lifting criterion, or is there another theorem that must be used?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member HappyJoe's Avatar
    Joined
    Sep 2010
    From
    Denmark
    Posts
    234
    I'm somewhat inexperienced, when it comes to covering spaces, but surely you want your 2-fold covering space to be connected? Otherwise you can just use the disjoint union of S^1\vee S^1 with itself.
    Last edited by HappyJoe; October 25th 2010 at 10:37 AM. Reason: LaTeX stuff
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2009
    Posts
    98
    I am not sure why it would have to be connected or not, and if not, why can I use this disjoint union?

    Is the Fundamental group of the wedge of two circles \pi _{1} ( S^1 V S^1),
    the free product of Z and Z (Z*Z)? If yes, how does this help find the nonequivalent 2-fold covering spaces of S^1 V S^1?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. covering spaces
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: July 18th 2011, 05:56 PM
  2. Covering spaces, R^n, homomorphism
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 21st 2011, 07:24 PM
  3. Covering spaces
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: December 7th 2010, 10:09 AM
  4. Homology & covering spaces
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: October 26th 2009, 07:11 PM
  5. Covering Spaces
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: September 28th 2009, 12:17 PM

Search Tags


/mathhelpforum @mathhelpforum