Topology

Poincaré Reconstructed — Article 1: A Purely Topological Resolution

Authors: Yuval Fradkin
Comments: 10 Pages. (Note by ai.viXra.org Admin: Please cite and list sceintific references)

This article introduces a topological approach to proving the Poincaré Conjecture in dimension 3. Unlike previous solutions that rely on geometric flows and curvature (notably Ricci flow), the approach here uses only tools from classical algebraic and geometric topology. The proof is based on the principle that every loop in a simply connected 3-manifold can be contracted within a locally embedded disc. This sets the foundation for a global classification that culminates in identifying the manifold with the 3-sphere.
Category: Topology