preprint

Inserted: 5 oct 2026

Year: 2026

Abstract:

We extend the classification of manifolds with positive isotropic curvature to all dimensions $n \geq 5$. This result also completes the classification of uniformly positive isotropic curvature on complete non-compact $κ$-noncollapsed ancient solutions and gradient shrinking Ricci solitons. The proof involves a construction of pinching cones in all dimensions, refining and extending to all dimensions the results of the first author. We have used MATHEMATICA to find viable parameters for the cone families. The final presentation is self-contained and can be verified manually. No stage of this work involved LLMs.