The Borel / Novikov conjectures and stable diffeomorphisms of 4-manifolds

@inproceedings{Davis2007TheB,
  title={The Borel / Novikov conjectures and stable diffeomorphisms of 4-manifolds},
  author={James F. Davis},
  year={2007}
}
Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S × S’s. This paper shows that two closed, orientable, homotopy equivalent, smooth 4-manifolds are stably diffeomorphic provided a certain map from the second homology of the fundamental group with coefficients in Z2 to the L-theory of the group is injective. This injectivity is implied by the Borel/Novikov conjecture for torsion-free groups, which is known for many groups. There are also results… CONTINUE READING