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Poincare conjecture?

  1. Nov 17, 2007 #1
    Does the Poincare conjecture say:

    Consider a compact 3-dimensional manifold V without boundary.

    Poincare conjectured that
    The fundamental group of V is trivial => V is homeomorphic to the 3-dimensional sphere?

    It has been proved for all manifolds except 3. However Perelman completed a proof that is almost certainly right for 3-manifolds, thereby proving Poincare to be right.

    My question is which fundamental group(s) does the statement refer to? i.e denoting pi for the fundamental group, pi_1 consists of 1 dimensional loops. pi_2 consists of 2-D strips...
     
    Last edited: Nov 17, 2007
  2. jcsd
  3. Nov 17, 2007 #2

    mathwonk

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    fundamental group always means pi1 not pi2.
     
  4. Nov 17, 2007 #3
    right. Have I stated the conjecture correctly?
     
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