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I heard this example was given in Whitehead's paper A CERTAIN OPEN MANIFOLD WHOSE GROUP IS UNITY.( http://qjmath.oxfordjournals.org/content/os-6/1/268.full.pdf ) But I was confused by his term. Thus I'm looking for an explanation in more standard terms about this example.

But since my aim is to know about an example of this kind, any alternative will do either.

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    $\begingroup$ @lethe: what is your question? What exactly would you like to know? (please reformulate your post so that it focuses on something specific that you would like to know). $\endgroup$
    – André Henriques
    Commented Nov 24, 2011 at 15:33
  • $\begingroup$ Sorry! I'm looking for a modern explanation about this example, but I wasn't so sure about whether the language is already "modern" in the original paper. Now it seems to be already settled...I didn't expect it can be just called "whitehead manifold"... Thanks all of you! $\endgroup$
    – Honglu
    Commented Nov 25, 2011 at 1:17

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It's discussed in Kirby's "The topology of 4-manifolds", around page 80, and at a glance the argument looks "modern".

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The manifold is the Whitehead manifold.

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  • $\begingroup$ See also J. Hempel - 3-Manifolds pag. 155 $\endgroup$
    – Francesco Lin
    Commented Nov 24, 2011 at 23:40
  • $\begingroup$ I didn't know it is given such a name. Thanks! If I had been able to accept both of the answers. $\endgroup$
    – Honglu
    Commented Nov 25, 2011 at 1:16

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