Paper · May 3, 2025
Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models
As on arXiv
Abstract
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 is a compact connected oriented -manifold with connected boundary , and if an unbounded number of disjoint copies of embed topologically and locally flatly in the interior of a compact -manifold then is a direct double, i.e., , 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 -manifold that embeds in is hyperbolic.
Comments: Correction to arXiv:1903.09181. Revised version of arXiv:2505.03823 with a new title. This version corrects an error in Proposition 13 of the earlier paper and establishes a more general result, giving a partial generalization of Hantzsche's theorem
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