Changes

===Formal Statement of the Conjecture===

===Formal Statement of the Conjecture===

For those readers who have taken undergraduate topology, the statement of the Poincare conjecture is much shorter:  

For those readers who have taken undergraduate topology, the statement of the Poincaré conjecture is much shorter:  

::''Let <math>X \ </math> be a <math>3 \ </math>-dimensional manifold.  Suppose that for every <math>m \leq 3 \ </math>, <math>\pi_m(X) \cong \pi_m(\mathbb{S}^3) \ </math>.  Does it follow that <math>X \ </math> is homeomorphic to <math>\mathbb{S}^3 \ </math>?

::''Let <math>X \ </math> be a <math>3 \ </math>-dimensional manifold.  Suppose that for every <math>m \leq 3 \ </math>, <math>\pi_m(X) \cong \pi_m(\mathbb{S}^3) \ </math>.  Does it follow that <math>X \ </math> is homeomorphic to <math>\mathbb{S}^3 \ </math>?