Homotopy invariance of 4-manifold decompositions: connected sums
classification
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math.AT
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assumingconjectureconnecteddecompositionsfundamentalgrouphomotopyborel
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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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