Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homology question

  1. Mar 5, 2009 #1

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    In Hatcher top of page 125, I do not understand where the first isomorphism comes from. He says it comes from the exact sequence of the pair, using the fact that CA is contractible, but what is the precise line of reasoning here?

    Hatcher's book: http://www.math.cornell.edu/~hatcher/AT/AT.pdf

    Thanks!
     
  2. jcsd
  3. Mar 5, 2009 #2
    Since CA is contractible [tex]\tilde{H}_n(CA)=0[/tex] for all n (there is a tilde over the H, but it's hard to see). Thus, if you write down the exact sequence of the pair [tex](X\cup CA,CA)[/tex] every third group in the sequence vanishes, which makes the two other groups isomorphic.
     
  4. Mar 5, 2009 #3

    quasar987

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I see, thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Homology question
  1. Simplicial homology (Replies: 2)

Loading...