Mathematics – Geometric Topology
Scientific paper
2004-06-04
Mathematics
Geometric Topology
Re-TeXed. The references are now numbered; Geometry and topology of manifolds, 63-76, Fields Inst. Commun., 47, Amer. Math. So
Scientific paper
Two 4-manifolds are stably diffeomorphic if they become diffeomorphic after connected sum with S^2 x S^2'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 Z/2 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 concerning the homotopy invariance of the Kirby-Siebenmann invariant. The method of proof is to use Poincare duality in Spin bordism to translate between Wall's classical surgery and Kreck's modified surgery.
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