On the 3-Dimensional Poincaré Conjecture and the 4-Dimensional Smooth Schoenflies Problem

2006/12/19 by Valentin Poénaru, Valentin Poenaru, Poenaru, Valentin
Mathematics · #57M10 #57M40 #57N60 #57Q10 #57R65 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Point processes and geometric inequalities #math.GT #msc:57M10 #msc:57M40 #msc:57N60 #msc:57Q10 #msc:57R65

paper · pdf · doi:10.48550/arxiv.math/0612554

arxiv created 2006/12/19 · openalex publication_date 2006/12/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This is the announcement of an alternative approach to the 3-dimensional Poincaré Conjecture, different from Perelman's big and spectacular breakthrough. No claim concerning the other parts of the Thurston Geometrization Conjecture, come with our purely 4-dimensional line of argument.

Related

• Poincare duality in dimension 3
• The Thurston's program derived from the Langlands global program with singularities
• Why a Conjecture of Poincare Doesn't Work
• On 4-dimensional smooth Poincare conjecture
• Hamilton-Perelman's Proof of the Poincaré Conjecture and the Geometrization Conjecture