Homotopy invariance of 4-manifold decompositions: connected sums

Details Homotopy invariance of 4-manifold decompositions: connected sums Homotopy invariance of 4-manifold decompositions: connected sums

2009-07-02

arxiv.org/abs/0907.0308v4

Mathematics

Geometric Topology

Scientific paper

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.

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