https://neckpinch.com/authors/michael-hartley-freedman/New arXiv papers by Michael Hartley Freedman, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2505.03823/arxiv:2505.03823Sat, 03 May 2025 00:00:00 GMTBennett Chow, Michael H. Freedman, Henry Shin, Yongjia Zhang — This note corrects an error in the proof of Proposition 13 in arXiv:1903.09181 and simultaneously establishes a more general result. We prove that if M is a compact connected oriented 4-manifold with connected boundary ∂M, and if an unbounded number of disjoint copies of M embed topologically and locally flatly in the interior of a compact 4-manifold N, then TorH₁(∂M;ℤ) is a direct double, i.e., TorH₁(∂M;ℤ)≅ A ⊕ A, with the linking pairing vanishing identically on the first summand, i.e., the linking pairing is split metabolic. This partially generalizes Hantzsche's theorem stating that the linking pairing for a closed 3-manifold that embeds in S⁴ is hyperbolic.Ricci solitonsSingularities4-manifolds