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For 3-dim Poincare Conjecture, the assumption is 'simply connected'. I am wondering whether simply connectedness assumption in 3-dim implies the same homopoy homotopy groups as the 3-sphere? or If we switch the assumption of 'simply connected' to 'homotopy 3-sphere', would it be easier to proof Poincare Conjecuture. |
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"homotopy shperesphere" assumption in Poincare Conjecture |
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"homotopy shpere" assumption in Poincare ConjectureFor 3-dim Poincare Conjecture, the assumption is 'simply connected'. I am wondering whether simply connectedness assumption in 3-dim implies the same homopoy groups as the 3-sphere? or If we switch the assumption of 'simply connected' to 'homotopy 3-sphere', would it be easier to proof Poincare Conjecuture.
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