Relationship To Other Conjectures
- The Borel conjecture implies the Novikov conjecture for the special case in which the reference map is a homotopy equivalence.
- The Poincaré conjecture asserts that a closed manifold homotopy equivalent to, the 3-sphere, is homeomorphic to . This is not a special case of the Borel conjecture, because is not aspherical. Nevertheless, the Borel conjecture for the 3-torus implies the Poincaré conjecture for .
Read more about this topic: Borel Conjecture
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