Two links at one point: an illustrated companion to the construction

This companion explains the construction in the accompanying manuscript Topological singularities in the codimension-two stratum of noncollapsed Ricci limits. The central distinction is between the fixed manifold that records the topology of a punctured neighbourhood and the limiting link that determines a metric tangent. We follow this distinction through the shrinking caps, the two volume normalizations, the radial curvature estimates, and the smooth filling procedure. The pictures locate the geometric pieces; exact formulas explain why their curvature remains controlled and why their topology can disappear in a tangent while remaining visible in every punctured neighbourhood. Illustrated companion to Topological singularities in the codimension-two stratum of noncollapsed Ricci limits. The deposit contains the companion PDF and an archive of its editable LaTeX source, figures, and reproducible figure generators.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-29
DOI
https://doi.org/10.5281/zenodo.23027761
Primary Topic
Mathematics, Computing, and Information Processing
Type
preprint
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preprint

Two links at one point: an illustrated companion to the construction

Anass NIFA
Zenodo (CERN European Organization for Nuclear Research)
Mathematics, Computing, and Information Processing
preprint

Two links at one point: an illustrated companion to the construction

Anass NIFA
preprint en

Abstract

This companion explains the construction in the accompanying manuscript Topological singularities in the codimension-two stratum of noncollapsed Ricci limits. The central distinction is between the fixed manifold that records the topology of a punctured neighbourhood and the limiting link that determines a metric tangent. We follow this distinction through the shrinking caps, the two volume normalizations, the radial curvature estimates, and the smooth filling procedure. The pictures locate the geometric pieces; exact formulas explain why their curvature remains controlled and why their topology can disappear in a tangent while remaining visible in every punctured neighbourhood. Illustrated companion to Topological singularities in the codimension-two stratum of noncollapsed Ricci limits. The deposit contains the companion PDF and an archive of its editable LaTeX source, figures, and reproducible figure generators.

Zenodo (CERN European Organization for Nuclear Research)
Sustainable cities and communities
Mathematics, Computing, and Information Processing
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