Homotopy invariance of 4-manifold decompositions: connected sums

Abstract

We show, up to h-cobordism, that the existence and uniqueness of connected sum decompositions of oriented 4-dimensional manifolds is an invariant of homotopy equivalence, assuming that the fundamental group of each summand is "good" in the sense of Freedman and Quinn. On a separate note, we observe that the Borel Conjecture is true in dimension 4 up to s-cobordism, assuming that the fundamental group satisfies the Farrell--Jones Conjecture.

14 pages, 1 figure, accepted by Topology and its Applications

References in corpus (4)

• Surgery on closed 4-manifolds with free fundamental group
• Manifolds homotopy equivalent to P^n # P^n
• On smoothable surgery for 4-manifolds
• On fibering and splitting of 5-manifolds over the circle

Cited by in corpus (4)

• Fillings of unit cotangent bundles
• Cancellation for 4-manifolds with virtually abelian fundamental group
• Fillings of unit cotangent bundles of nonorientable surfaces
• Topological 4-manifolds with 4-dimensional fundamental group