The Borel/Novikov conjectures and stable diffeomorphisms of 4-manifolds
Abstract
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.
Cite
@article{arxiv.math/0406084,
title = {The Borel/Novikov conjectures and stable diffeomorphisms of 4-manifolds},
author = {James F. Davis},
journal= {arXiv preprint arXiv:math/0406084},
year = {2015}
}
Comments
Re-TeXed. The references are now numbered; Geometry and topology of manifolds, 63-76, Fields Inst. Commun., 47, Amer. Math. Soc., Providence, RI, 2005