Another way of answering Henri Poincare's fundamental question

2010/01/23 by Peter Mani-Levitska, Mani-Levitska, Peter
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.DG

paper · pdf · doi:10.48550/arxiv.1001.4164

13 pages, 1 figure

arxiv created 2010/01/23 · openalex publication_date 2010/01/23 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

After G. Perelman's solution of the Poincare Conjecture, this is a different way toward it. Given a simply connected, closed 3-manifold M, we produce a homotopy disc H, which arises from M by a finite sequence of simple modifications and, almost miraculously, can be imbedded into the ordinary space R³. It follows that H is a disc, hence M is a sphere. In order to construct H, we use a special stratification of M, based on the fact that M is simply connected.

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