Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

Bennett Chow; Michael H. Freedman; Henry Shin; Yongjia Zhang

Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

Differential Geometry 2026-03-30 v2 Algebraic Topology Geometric Topology

Authors: Bennett Chow , Michael H. Freedman , Henry Shin , Yongjia Zhang

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 $M$ is a compact connected oriented $4$ -manifold with connected boundary $\partial M$ , 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 $\operatorname{Tor}H_1(\partial M;\mathbb{Z})$ is a direct double, i.e., $\operatorname{Tor}H_1(\partial M;\mathbb{Z})\cong A \oplus A$ , 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 $S^4$ is hyperbolic.

Keywords

gradient Ricci soliton singularity model 4-manifold linking pairing split metabolic Hantzsche theorem topological embedding

Cite

@article{arxiv.2505.03823,
  title  = {Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models},
  author = {Bennett Chow and Michael H. Freedman and Henry Shin and Yongjia Zhang},
  journal= {arXiv preprint arXiv:2505.03823},
  year   = {2026}
}

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

Correction to: Curvature growth of some 4-dimensional gradient Ricci soliton singularity models

Abstract

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